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Chapter 15: Problem 18

Hiking in the mountains, you shout "hey," wait \(2.00 \mathrm{~s}\) and shout again. What is the distance between the sound waves you cause? If you hear the first echo after \(5.00 \mathrm{~s}\), what is the distance between you and the point where your voice hit a mountain?

Short Answer

Expert verified
Answer: The distance between the person and the point where their voice hits the mountain is 857.5 meters.

Step by step solution

01

Find the speed of sound in air

The typical speed of sound in air at room temperature (20 degrees Celsius) is approximately 343 meters per second (m/s). We'll use this speed in our calculations.
02

Calculate the distance between the sound waves

To find the distance between the two sound waves caused by the shouts, we can use the formula distance = speed * time. We know the time between the shouts is 2 seconds, and we already know the speed of sound in air. Therefore, we can calculate the distance like this: Distance = 343 m/s * 2 s Distance = 686 meters So, the distance between the two sound waves is 686 meters.
03

Calculate the round-trip time for the echo

The problem states that the first echo is heard after 5 seconds. This means that the sound has traveled to the mountain and then back to the person. To find the time it takes for the sound to reach the mountain, we need to divide the total time by 2: Time to reach the mountain = 5 s / 2 = 2.5 s
04

Calculate the distance between the person and the mountain

Now that we know the time it takes for the sound to travel to the mountain, we can use the same formula, distance = speed * time, to find the distance between the person and the mountain: Distance = 343 m/s * 2.5 s Distance = 857.5 meters So, the distance between the person and the mountain is 857.5 meters.

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Most popular questions from this chapter

A sinusoidal wave traveling in the positive \(x\) -direction has a wavelength of \(12 \mathrm{~cm},\) a frequency of \(10.0 \mathrm{~Hz},\) and an amplitude of \(10.0 \mathrm{~cm}\). The part of the wave that is at the origin at \(t=0\) has a vertical displacement of \(5.00 \mathrm{~cm} .\) For this wave, determine the a) wave number, d) speed, b) period, e) phase angle, and c) angular frequency, f) equation of motion.

A 2.00 -m-long string of mass \(10.0 \mathrm{~g}\) is clamped at both ends. The tension in the string is \(150 \mathrm{~N}\). a) What is the speed of a wave on this string? b) The string is plucked so that it oscillates. What is the wavelength and frequency of the resulting wave if it produces a standing wave with two antinodes?

A \(3.00-\mathrm{m}\) -long string, fixed at both ends, has a mass of \(6.00 \mathrm{~g}\). If you want to set up a standing wave in this string having a frequency of \(300 . \mathrm{Hz}\) and three antinodes, what tension should you put the string under?

A string with linear mass density \(\mu=0.0250 \mathrm{~kg} / \mathrm{m}\) under a tension of \(T=250 . \mathrm{N}\) is oriented in the \(x\) -direction. Two transverse waves of equal amplitude and with a phase angle of zero (at \(t=0\) ) but with different frequencies \((\omega=3000\). rad/s and \(\omega / 3=1000 . \mathrm{rad} / \mathrm{s}\) ) are created in the string by an oscillator located at \(x=0 .\) The resulting waves, which travel in the positive \(x\) -direction, are reflected at a distant point, so there is a similar pair of waves traveling in the negative \(x\) -direction. Find the values of \(x\) at which the first two nodes in the standing wave are produced by these four waves.

Consider a linear array of \(n\) masses, each equal to \(m,\) connected by \(n+1\) springs, all massless and having spring constant \(k\), with the outer ends of the first and last springs fixed. The masses can move without friction in the linear dimension of the array. a) Write the equations of motion for the masses. b) Configurations of motion for which all parts of a system oscillate with the same angular frequency are called normal modes of the system; the corresponding angular frequencies are the system's normal-mode angular frequencies. Find the normal-mode angular frequencies of this array.
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