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Chapter 11: Problem 14

What is the frequency of a wave whose speed and wavelength are $120 \mathrm{m} / \mathrm{s}\( and \)30.0 \mathrm{cm},$ respectively?

Short Answer

Expert verified
Answer: The frequency of the wave is 400 Hz.

Step by step solution

01

Write down the given values

The wave speed is \(120 \mathrm{m/s}\) and the wavelength is \(30.0 \mathrm{cm}\). To make our calculations easier, let's convert the wavelength to meters: \(30.0 \mathrm{cm} = 0.3 \mathrm{m}\).
02

Write the wave speed formula

The wave speed formula is given by: wave speed = frequency x wavelength or \(v = f位\), where \(v\) represents the wave speed, \(f\) the frequency, and \(位\) the wavelength.
03

Isolate the frequency in the formula

We want to find the frequency, so we need to isolate it in the wave speed formula. Divide both sides of the equation by the wavelength to get: \(f = \frac{v}{位}\).
04

Plug in the values and calculate the frequency

We have the given values and the formula to calculate the frequency. Plug in the values, \(v = 120 \mathrm{m/s}\) and \(位 = 0.3 \mathrm{m}\), into the formula: \(f = \frac{120 \mathrm{m/s}}{0.3 \mathrm{m}}\).
05

Solve the equation

Solve the equation for \(f\): \(f = \frac{120}{0.3} \mathrm{s^{-1}} = 400 \mathrm{s^{-1}}\). The frequency of the wave is \(400 \mathrm{Hz}\).

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Most popular questions from this chapter

Periodic Waves What is the speed of a wave whose frequency and wavelength are $500.0 \mathrm{Hz}\( and \)0.500 \mathrm{m},$ respectively?
The equation of a wave is $$ y(x, t)=(3.5 \mathrm{cm}) \sin \left\\{\frac{\pi}{3.0 \mathrm{cm}}[x-(66 \mathrm{cm} / \mathrm{s}) t]\right\\} $$ Find (a) the amplitude and (b) the wavelength of this wave.
A transverse wave on a string is described by $y(x, t)=(1.2 \mathrm{cm}) \sin [(0.50 \pi \mathrm{rad} / \mathrm{s}) t-(1.00 \pi \mathrm{rad} / \mathrm{m}) x]$ Find the maximum velocity and the maximum acceleration of a point on the string. Plot graphs for displacement \(y\) versus \(t\), velocity \(v_{y}\) versus \(t\), and acceleration \(a_{y}\) versus \(t\) at \(x=0.\)
A uniform string of length \(10.0 \mathrm{m}\) and weight \(0.25 \mathrm{N}\) is attached to the ceiling. A weight of \(1.00 \mathrm{kN}\) hangs from its lower end. The lower end of the string is suddenly displaced horizontally. How long does it take the resulting wave pulse to travel to the upper end? [Hint: Is the weight of the string negligible in comparison with that of the hanging mass?]
For a transverse wave on a string described by $y(x, t)=(0.0050 \mathrm{m}) \cos [(4.0 \pi \mathrm{rad} / \mathrm{s}) t-(1.0 \pi \mathrm{rad} / \mathrm{m}) x]$ find the maximum speed and the maximum acceleration of a point on the string. Plot graphs for one cycle of displacement \(y\) versus \(t\), velocity \(v_{y}\) versus \(t\), and acceleration \(a_{y}\) versus \(t\) at the point \(x=0.\)
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