# High School Physics : Properties of Waves

## Example Questions

### Example Question #1 : Properties Of Waves

After exercising, Jane takes her pulse. She realizes that her heart is beating rapidly, approximately four beats every second. What is the period of her elevated heart rate?

Explanation:

When you see a relationship like "times every second" or "once per hour," these are hints you are looking at a frequency. Frequency is, effectively, how often something happens. If it happens four times per second, then we know how often it happens. The units "per second" are equivalent to Hertz.

The relationship between frequency and period is .

Since our given frequency was four beats per second, or , we can solve for the period.

This means that her heart beats once every  seconds.

### Example Question #2 : Properties Of Waves

A wave oscillates with a speed of  and has a wavelength of . What is the frequency of the wave?

Explanation:

The equation for velocity in terms of wavelength and frequency is .

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

### Example Question #3 : Properties Of Waves

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

There is insufficient information to solve.

The new wavelength will also double.

The new wavelength will be 12  the old wavelength.

The wavelengths will be the same.

The new wavelength will be 12  the old wavelength.

Explanation:

The relationship between velocity, frequency, and wavelength is:

In this case we're given a scenario where  and . The velocities equal each other because the problem states it has a constant velocity. Therefore we can set these equations equal to each other:

Notice that the f's cancel out:

Divide both sides by two:

### Example Question #4 : Properties Of Waves

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

We need to know the period in order to solve

They have the same wavelength

Explanation:

The relationship between frequency and wavelength determines the velocity:

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

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.

We are told that . Substitute into our equation.

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

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.

### Example Question #5 : Properties Of Waves

A wave has a frequency of . What is its period?

Explanation:

The relationship between frequency and period is .

Plug in our given value:

### Example Question #6 : Properties Of Waves

What is the wavelength of the wave above?

Explanation:

The wavelength of a wave is defined as the distance from a point on the wave to the same point on the wave (crest to crest or trough to trough). The distance between peaks is .

### Example Question #7 : Properties Of Waves

What is the amplitude of the wave above?

Explanation:

The amplitude of wave is defined as the distance the wave displaces from the equilibrium point.  In this case, the wave displaces  from the axis (the equilibrium point).

### Example Question #981 : High School Physics

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 stays the same

It increases

It decreases

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.

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

### Example Question #982 : High School Physics

Resonance in a system, such as a string fixed at both ends, occurs when

It is oscillating in simple harmonic motion

Its frequency is the same as the frequency of the external source

Its frequency is less than the frequency of the external source

Its frequency is greater than the frequency of the external source