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Home » Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of the S wave is about , and that of the wave is . A seismograph records and waves from an earthquake. The first P wave arrives 4 min before the first wave. Assuming the waves travel in a straight line, at what distance does the earthquake occur?
Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of the S wave is about 4.0 \mathrm{~km} \mathrm{~s}^{-1}, and that of the \mathrm{P} wave is 8.0 \mathrm{~km} \mathrm{~s}^{-1}. A seismograph records \mathrm{P} and \mathrm{S} waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in a straight line, at what distance does the earthquake occur?
CBSE | Class 11 | NCERT | Physics | Waves
Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of the S wave is about 4.0 \mathrm{~km} \mathrm{~s}^{-1}, and that of the \mathrm{P} wave is 8.0 \mathrm{~km} \mathrm{~s}^{-1}. A seismograph records \mathrm{P} and \mathrm{S} waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in a straight line, at what distance does the earthquake occur?

Let S and P have speeds of v_{1} and v_{2}, respectively. The S and P waves take t_{1} and t_{2} seconds to reach the position of the seismograph, respectively.

I=v_{1} t_{1}=v_{2} t_{2}

The speed of S wave is given as v_{1}=4.0 \mathrm{~km} \mathrm{~s}^{-1}

The speed of P wave is given as v_{2}=8.0 \mathrm{~km} \mathrm{~s}^{-1}

\begin{array}{l} 4 t_{1}=8 t_{2} \\ t_{1}=2 t_{2} \end{array}

The first \mathrm{P} wave arrives 4 \mathrm{~min} before the \mathrm{S} wave.

\begin{array}{l} t_{1}-t_{2}=4 \min =4 \times 60 \mathrm{~s}=240 \mathrm{~s} \\ 2 \mathrm{t}_{2}-\mathrm{t}_{2}=240 \mathrm{~s} \\ \mathrm{t}_{2}=240 \mathrm{~s} \\ \mathrm{t}_{1}=2 \mathrm{t}_{2}=2 \times 240=480 \mathrm{~s} \end{array}

Distance at which earthquake occur willbe,

\mathrm{I}=\mathrm{v}_{1} \mathrm{t}_{1}=4 \times 480=1920 \mathrm{~km}

i

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