Physics
Physics
3rd Edition
ISBN: 9781259233616
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 11, Problem 82P

(a)

To determine

An equation for a surface seismic wave.

(a)

Expert Solution
Check Mark

Answer to Problem 82P

An equation for a surface seismic wave is y(x,t)=(0.020m)sin((1.6rad/s)t+(0.0016rad/m)x).

Explanation of Solution

The wave is moving is x axis. The amplitude of the wave is 2.0cm. The period of the wave is 4.0s. The wave length of the wave is 4.0km. The wave is considered to be harmonic.

Write the formula for the equation of a harmonic wave.

y(x,t)=Asin(ωt+kx) (I)

Here, y is the displacement, A is the amplitude, ω is the angular speed, t is the time, k is the propagation vector, x is the distance travelled by the wave.

Write the formula for ω in terms of time period.

ω=2πT (II)

Here, T is the time period.

Write the formula for k in terms of wavelength.

k=2πλ (III)

Here, λ is the wavelength.

Substitute equation (II) and (III) in equation (I).

y(x,t)=Asin(2πtT+2πxλ) (IV)

Conclusion:

Substitute 2.0cm for A, 4.0s for T, 4.0km for λ in equation (IV).

y(x,t)=(2.0cm)sin(2πt4.0s+2πx4.0km)=(20×102m)sin(2πt4.0s+2πx4.0×103m)=(0.020m)sin((1.6rad/s)t+(0.0016rad/m)x)

An equation for a surface seismic wave is y(x,t)=(0.020m)sin((1.6rad/s)t+(0.0016rad/m)x).

(b)

To determine

The maximum speed of ground as the wave pass by it.

(b)

Expert Solution
Check Mark

Answer to Problem 82P

The maximum speed of ground as the wave pass by it is 0.031m/s.

Explanation of Solution

The wave is moving is x axis. The amplitude of the wave is 2.0cm. The period of the wave is 4.0s. The wave length of the wave is 4.0km. The wave is considered to be harmonic.

Write the formula for the maximum speed of the ground as the wave pass by.

vm=ωA=2πAT (V)

Here, vm is the maximum speed, A is the amplitude, ω is the angular speed, T is the time period.

Conclusion:

Substitute 2.0cm for A, 4.0s for T in equation (V).

vm=2π(2.0cm)4.0s=2π(2.0×102m)4.0s=0.031m/s

The maximum speed of ground as the wave pass by it is 0.031m/s.

(c)

To determine

The speed of the wave.

(c)

Expert Solution
Check Mark

Answer to Problem 82P

The speed of the wave is 1.0km/s.

Explanation of Solution

The wave is moving is x axis. The amplitude of the wave is 2.0cm. The period of the wave is 4.0s. The wave length of the wave is 4.0km. The wave is considered to be harmonic.

Write the formula for the speed of the propagation of the wave.

v=λf=λT (VI)

Here, v is the propagation speed of the wave, λ is the wavelength, f is the frequency, T is the time period.

Conclusion:

Substitute 4.0km for λ, 4.0s for T in equation (VI).

v=4.0km4.0s=1.0km/s

The speed of the wave is 1.0km/s.

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Chapter 11 Solutions

Physics

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