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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 \(v = fλ\), where \(v\) represents the wave speed, \(f\) the frequency, and \(λ\) 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: \(f = \frac{v}{λ}\).
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 \(λ = 0.3 \mathrm{m}\), 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

Light visible to humans consists of electromagnetic waves with wavelengths (in air) in the range \(400-700 \mathrm{nm}\) $\left(4.0 \times 10^{-7} \mathrm{m} \text { to } 7.0 \times 10^{-7} \mathrm{m}\right) .$ The speed of light in air is \(3.0 \times 10^{8} \mathrm{m} / \mathrm{s} .\) What are the frequencies of electromagnetic waves that are visible?
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 \(x=0.\)
Write the equation for a transverse sinusoidal wave with a maximum amplitude of \(2.50 \mathrm{cm}\) and an angular frequency of 2.90 rad/s that is moving along the positive \(x\) -direction with a wave speed that is 5.00 times as fast as the maximum speed of a point on the string. Assume that at time \(t=0,\) the point \(x=0\) is at \(y=0\) and then moves in the \(-y\) -direction in the next instant of time.
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.
What is the speed of the wave represented by \(y(x, t)=\) $A \sin (k x-\omega t),\( where \)k=6.0 \mathrm{rad} / \mathrm{cm}\( and \)\omega=5.0 \mathrm{rad} / \mathrm{s} ?$
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