Physics - Waves | Practice Hub

A piano tuner hears one beat every when trying to adjust two strings, one of which is sounding . How far off in frequency is the other string?

Explanation

We can calculate the frequency of the beat using the equation

$f = \frac{1}{T}$

$f = \frac{1}{2s}$

This is the beat frequency which means that the other string is off by either higher or lower.

Two notes are played simultaneously. One of them has a period of and the other has a period of . Which one has a longer wavelength?

We need to know the frequency in order to solve

They have the same wavelength

We need to know the period in order to solve

Explanation

The relationship between frequency and wavelength determines the velocity:

$v= \lambda f$

The frequency is the inverse of the period. We can substitute this into the equation above.

$v= \lambda 1/T$

In the question, both of the notes are played at the same time in the same location, so they both should have the same velocity. We can set the equation for each tone equal to each other.

$\lambda _1(1/T_1)= \lambda _2(1/T_2)$

We are told that . Substitute into our equation.

$\lambda _1(1/T_1)= \lambda _2(1/(2T_1)$

We can cancel the period from each side of the equation, leaving the relationship between the two wavelengths.

$\lambda _1=( \frac{1}{2}) \lambda _2$

The wavelength of the first wave is equal to half the wavelength of the second. This means that the wavelength for the tone with a longer period will have a longer wavelength as well.

In seismology, the wave is a transverse wave. As an wave travels through the Earth, the relative motion between the wave and the particles is

Parallel

Perpendicular

First parallel, then perpendicular

First perpendicular, then parallel

Explanation

Transverse waves are waves whose particles travel perpendicular to the direction that the wave itself is traveling. Electromagnetic waves are another example of transverse waves.

Two waves, one with an amplitude of and the other of are superimposed with destructive interference. What is the resultant amplitude?

Explanation

When two waves are superimposed, the interference can be either constructive or destructive. In this case the interference is destructive, which means our resultant amplitude will be the difference of the two given amplitudes.

That means our new amplitude will be .

A student attaches one end of a Slinky to the top of a table. She holds the other end in her hand, stretches it to a length , and then moves it back and forth to send a wave down the Slinky. If she next moves her hand faster while keeping the length of the Slinky the same, how does the wavelength down the slinky change?

It increases

It stays the same

It decreases

Explanation

The speed of the wave along the Slinky depends on the mass of the Slinky itself and the tension caused by stretching it. Since both of these things have not changed, the wave speed remains constant.

The wave speed is equal to the wavelength multiplied by the frequency.

$v = \lambda f$

Since she is moving her hand faster, the frequency has increased. Since the velocity has not changed, an increase in the frequency would decrease the wavelength.

Order the following electromagnetic waves from the longest wavelength to the shortest: Gamma Rays, Infrared, Microwaves, Radio Waves, Ultraviolet, Visible Light, X-Rays

Radio Waves, Gamma Rays, Microwaves, Infrared, Visible Light, X-Rays, Ultraviolet

Gamma Rays, Infrared, Microwaves, Radio Waves, Ultraviolet, Visible Light, X-Rays

Radio Waves, Microwaves, Infrared, Visible Light, Ultraviolet, X-Rays, Gamma Rays

Visible Light, Infrared, Microwaves, Gamma Rays, X-Rays, Ultraviolet, Radio Waves

Gamma Rays, X-Rays, Ultraviolet, Visible Light, Infrared, Microwaves, Radio Waves

Explanation

Radio waves have the smallest frequency and longest wavelength. This is why they are not dangerous. Microwaves have the next longest wavelength and are what are used to warm up cold foods. Infrared waves are the next longest wavelength and border the red light on the visible spectrum. Infrared waves are used in remote controls and night vision. Visible light is next and is what we can see with our eyes. Next is ultraviolet, which borders the violet light on the visible spectrum. These are the damaging rays by the sun and are essentially “super-violet” rays. Next is X-rays. These have very high frequencies and are dangerous in high quantities. Gamma rays are the shortest wavelength and the highest frequency and the most dangerous. These cosmic rays often come from stars and other celestial objects.

In seismology, the wave is a transverse wave. As an wave travels through the Earth, the relative motion between the wave and the particles is

Parallel

First perpendicular, then parallel

First parallel, then perpendicular

Perpendicular

Explanation

Transverse waves are waves whose particles travel perpendicular to the direction that the wave itself is traveling. Electromagnetic waves are another example of transverse waves.

A wave oscillates with a speed of $8.9\frac{m}{s}$ and has a wavelength of . What is the frequency of the wave?

Explanation

The equation for velocity in terms of wavelength and frequency is $v=\lambda f$ .

We are given the velocity and the wavelength. Using these values, we can solve for the frequency.

$v=\lambda f$

$8.9\frac{m}{s}=6.7m* f$

$\frac{8.9\frac{m}{s}}{6.7m}=f$

A wave with a constant velocity doubles its frequency. What happens to its wavelength?

The new wavelength will be $\frac{1}{2}$ the old wavelength.

The new wavelength will also double.

The wavelengths will be the same.

There is insufficient information to solve.

Explanation

The relationship between velocity, frequency, and wavelength is:

$v=f\lambda$

In this case we're given a scenario where $v=f\lambda_1$ and $v=2f*\lambda_2$ . The velocities equal each other because the problem states it has a constant velocity. Therefore we can set these equations equal to each other: