a) 4 m b) 0.5 m c) λ/2 d) 3 λ/4 e) what is the phase difference between the oscillation of a particle located at x = 100 cm at t = Ts and t = 5s? Answer: According to the questions, we have: y = 2...
In the given progressive waves y = 5 sin (100 πt – 0.4 πx) where y and x are in m, t is in s. What is the
a) amplitude b) wavelength Answer: According to the question, the wave is travelling in +x direction and the equation is given by; y = 5 sin (100 πt – 0.4 πx) The standard equation is as follows: y...
Given below are some functions of x and t to represent the displacement of an elastic wave.
a) y = 5 cos (4x) sin (20t) b) y = 4 sin (5x-t/2) + 3 cos (5x-t/2) c) y = 10 cos [(252-250)πt] cos [(252+250) πt] d) y = 100 cos (100 πt + 0.5x) State which of these represent a) a traveling wave...
If c is r.m.s speed of molecules in a gas and v is the speed of sound waves in the gas, show that c/v is constant and independent of temperature for all diatomic gases.
Answer: We know that the equation for molecules is: $ c=\sqrt{\frac{3RT}{M}} $ Where, M represents the molar mass of the gas $ v=\sqrt{\frac{\gamma P}{\rho }}=\sqrt{\frac{\gamma RT}{M}} $ We know...
The earth has a radius of 6400 km. The inner core of the 1000 km radius is solid. Outside it, there is a region from 1000 km to a radius of 3500 km which is in a molten state. Then again from 3500 km to 6400 km the earth is solid. Only longitudinal (P) waves can travel inside a liquid. Assume that the P wave has a speed of 8 km/s in solid parts and of 5 km/s in liquid parts of the earth. An earthquake occurs at someplace close to the surface of the earth. Calculate the time after which it will be recorded in a seismometer at a diametrically opposite point on the earth if wave travels along diameter?
Answer: According to the question, r1 = 1000 km, r2 = 3500 km, r3 = 6400 km and d1 = 1000 km And we can calculate, d2 = 3500 – 1000 d2 = 2500 km d3 = 6400 – 3500 d3 = 2900 km Expression for the...
Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops, and 4 loops, the frequencies are in the ratio 1:2:3:4.
Answer: When n = 1, f1 = v/2L This is known as the fundamental frequency. When n = 2, f2 = 2(v/2L) This is known as the first overtone. When n = 3, f3 = 3(v/2L) This is known as the second overtone....
A tuning fork vibrating with a frequency of 512 Hz is kept close to the open end of a tube filled with water. The water level in the tube is gradually lowered. When the water level is 17 cm below the open end, the maximum intensity of sound is heard. If the room temperature is 20oC, calculate
c) if the water in the tube is replaced with mercury, will there be any difference in your observations? Answer: (c) Sound is reflected into the air column by water and mercury in the tube, forming...
A tuning fork vibrating with a frequency of 512 Hz is kept close to the open end of a tube filled with water. The water level in the tube is gradually lowered. When the water level is 17 cm below the open end, the maximum intensity of sound is heard. If the room temperature is 20oC, calculate
a) speed of sound in air at room temperature b) speed of sound in air at 0oC Answer: According to the question, the frequency of the tuning fork is f = 512 Hz a) When the first maxima are taken...
The pattern of standing waves formed on a stretched string at two instants of time are shown in the figure. The velocity of two waves superimposing to form stationary waves is 360 m/s and their frequencies are 256 Hz.
a) calculate the time at which the second curve is plotted b) mark nodes and antinodes on the curve c) calculate the distance between A’ and C’ Answer: According to the quetion, the frequency of the...
The wave pattern on a stretched string is shown in the figure. Interpret what kind of wave this is and find its wavelength.
Answer: A stationary wave which is at its mean position when the particles at t = T/4 and 3T/4 are at rest. The displacement of medium particles at distances of 10, 20, 30, 40, and 50 cm is always...
A train standing at the outer signal of a railway station blows a whistle of frequency 400 Hz still air. The train beings to move with a speed of 10 m/s towards the platform. What is the frequency of the sound for an observer standing on the platform?
Answer: It is given that v0 = 400 Hz and vz = 10 m/s We know that the velocity of sound in air is va = 330 m/s The frequency heard by the observer on the platform is v'. Therefore, we can write: v’...
A pipe of 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of 1237.5 Hz?
Answer: According to the question, the length is: l = 20 cm =0.2 m and the frequency is, v = 1237.5 Hz We know that the velocity of sound in air = 330 m/s The following expression is: l = λ/4 λ = 4l...
A steel wire has a length of 12 m and a mass of 2.10 kg. What will be the speed of a transverse wave on this wire when a tension of 2.06 × 104 N is applied?
Answer: According to the question, the length is, l = 12 m and the total mass, M = 2.10 kg Mass per unit length is given by7 m = M/l = 2.1/12 and we know that tension si: T = 2.06 × 104 N Therefore,...
When two waves of almost equal frequencies v1 and v2 reach at a point simultaneously, what is the time interval between successive maxima?
Answer: Beats are created when two waves of nearly identical frequency arrive at the same location at the same time. It is given that the two frequencies are almost equal, that is v1 = v2. And for...
At what temperatures will the speed of sound in air be 3 times its value at 0 degreesC?
Answer: Speed of sound in air is $ v=\sqrt{\frac{\gamma RT}{M}} $ where 'T' represents the absolute temperature. since both γ and M are constant, we can write: $ \therefore v\alpha \sqrt{T} $ $...
A sitar wire is replaced by another wire of same length and material but of three times earlier radius. If the tension in the wire remains the same, by what factor will the frequency change?
Answer: The wire is stretched both from the end so the frequency of stretched wire is as follows: $ v=\frac{n}{2L}\sqrt{\frac{T}{m}} $ As the number of harmonic n, length L, and tension (T) are kept...
The displacement of an elastic wave is given by the function y = 3 sin ωt + 4 cos ωt where y is in cm and t is in second. Calculate the resultant amplitude.
Answer: According to the question, y = 3 sin ωt + 4 cos ωt Let’s suppose that 3 = a cos φ and 4 = a sin φ Then, the equation becomes: y = a cos φ ωt + a sin φ ωt y = a sin (ωt + φ) tan φ = 4/3 φ =...
An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?
Answer: Because the medium, frequency, and number of harmonics are the same in open and closed pipes, the number of nodes and (wave) will be the same in both circumstances. When the harmonic is...
A sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same, the length of the wire is doubled. Under what conditions would the tuning fork still be is resonance with the wire?
Answer: When a sonometer vibrates, the length of the wire is doubled. The sonometer will resonate at 2L if the tuning fork resonates at L. The frequency of the sonometer is expressed using the...
A tuning fork A, marked 512 Hz, produces 5 beats per second, where sounded with another unmarked tuning fork B. If B is loaded with wax the number of beats is again 5 per second. What is the frequency of the tuning fork B when not loaded?
Answer: When the tuning fork B is loaded with wax, the tuning fork's frequency falls below its original frequency. Let's say that when the tuning fork is marked 512 Hz, the tuning fork B is marked...
Which of the following statements are true for a stationary wave?
a) every particle has a fixed amplitude which is different from the amplitude of its nearest particle b) all the particles cross their mean position at the same time c) all the particles are...
A train, standing in a station yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10 m/s. Given that the speed of sound in still air is 340 m/s
a) the frequency of sound as heard by an observer standing on the platform is 400 Hz b) the speed of sound for the observer standing on the platform is 350 m/s c) the frequency of sound as heard by...
The transverse displacement of a string is given by y(x,t) = 0.06 sin (2πx/3) cos (120πt). All the points on the string between two consecutive nodes vibrate with
a) same frequency b) same phase c) same energy d) different amplitude Answer: The correct answers are a) same frequency b) same phase d) different amplitude Explanation: This is the standing wave...
During propagation of a plane progressive mechanical wave
a) all the particles are vibrating in the same phase b) amplitude of all the particles is equal c) particles of the medium executes SHM d) wave velocity depends upon the nature of the medium Answer:...
Speed of sound waves in a fluid depends upon
a) directly on the density of the medium b) square of bulk modulus of the medium c) inversely on the square root of density d) directly on the square root of bulk modulus of the medium Answer: The...
The displacement of a string is given by y(x,t) = 0.06 sin (2πx/3) cos (120πt) where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 × 10-2kg.
a) it represents a progressive wave of frequency 60 Hz b) it represents a stationary wave of frequency 60 Hz c) it is the result of the superposition of two waves of wavelength 3 m, frequency 60 Hz...
A transverse harmonic wave on a string is described by y (x,t) = 3.0 sin (36t + 0.018x + π/4) where x and y are in cm and t is in s. The positive direction of x is from left to right
a) the wave is travelling from right to left b) the speed of the wave is 20 m/s c) frequency of the wave is 5.7 Hz d) the least distance between two successive crests in the wave is 2.5 cm Answer:...
A train whistling at constant frequency is moving towards a station at a constant speed V. The train goes past a stationary observer on the station. The frequency n’ of the sound as heard by the observer is plotted as a function of time t. Identify the expected curve
Answer: The correct option is c) Explanation: Apparent Frequency can be expressed in a variety of ways. Assume that the observer (O) and the source (S) are both traveling in the same direction down...
A string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in
a) one second b) 0.5 second c) 2 seconds d) data given is insufficient Answer: The correct option is b) 0.5 second Explanation: According to the question, m=2.50 kg, l = 20 m and T=200N $ \mu...
Equation of a plane progressive wave is given by y = 0.6 sin 2π(t-x/2). On reflection from a denser medium, its amplitude becomes 2/3 of the amplitude of the incident wave
a) y = 0.6 sin 2π(t+x/2) b) y = -0.4 sin 2π(t+x/2) c) y = 0.4 sin 2π(t+x/2) d) y = -0.4 sin 2π(t-x/2) Answer: The correct option is b) y = -0.4 sin 2π(t+x/2) Explanation: The amplitude of the...
A sound wave is passing through the air column in the form of compression and rarefaction. In consecutive compressions and rarefactions,
a) density remains constant b) Boyle’s law is obeyed c) bulk modulus of air oscillates d) there is no transfer of heat Answer: The correct option is d) there is no transfer of heat Explanation:...
Which of the following statements are true for wave motion?
a) mechanical transverse waves can propagate through all mediums b) longitudinal waves can propagate through solids only c) mechanical transverse waves can propagate through solids only d)...
With the propagation of longitudinal waves through a medium, the quantity transmitted is
a) matter b) energy c) energy and matter d) energy, matter, and momentum Answer: The correct option is b) energy The transfer of energy across a medium is caused by longitudinal waves propagating...
Change in temperature of the medium changes
a) frequency of sound waves b) amplitude of sound waves c) wavelength of sound waves d) loudness of sound waves Answer: The correct option is c) wavelength of sound waves Explanation: The velocity...
Speed of sound wave in air
a) is independent of temperature b) increases with pressure c) increases with an increase in humidity d) decreases with an increase in humidity Answer: The correct option is c) increases with an...
Sound waves of wavelength λ travelling in a medium with a speed of v m/s enter into another medium where its speed is 2v m/s. The wavelength of sound waves in the second medium is
a) λ b) λ/2 c) 2 λ d) 4 λ Answer: The correct answer is c) 2 λ Explanation: According to the question, the wavelength of sound waves in the first medium, λ = u/v ...
Water waves produced by a motorboat sailing in water are
a) neither longitudinal nor transverse b) both longitudinal and transverse c) only longitudinal d) only transverse Answer: The correct option is b) both longitudinal and transverse Let's...