Question

ASAP PLease i need your help with these 100 points
Sally sits and observes an ocean wave
She times waves and finds that it takes 32.8 s for 6.00 waves to pass by. What is the period of the wave?

What is the frequency of the wave?

She also notices that there is a distance of 1.82 m between crests. What is the wavelength of the wave?

Finally, she records that from the highest point on a wave to the lowest point is a distance of 0.742 m. What is the amplitude of the wave?

Calculate the velocity of the wave.

Answer 1

1) 5.47 s

2) 0.183 Hz

3) 1.82 m

4) 0.371 m

5) 0.333 m/s

Explanation:

1)

The period of a wave is the time it takes for the wave to make one complete oscillation.

The period of a wave can be calculated as follows:

$T=\frac{t}{N}$

where

N is the number of oscillations of the wave

t is the time taken for N oscillations to occur

For the wave in this problem:

N = 6.00 is the number of oscillations

t = 32.8 s is the time taken

Substituting, we find the period:

$T=\frac{32.8}{6.00}=5.47 s$

2)

The frequency of a wave is number of complete oscillations of the wave per unit time.

The frequency of wave can be calculated from its period using the relationship:

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

where

f is the frequency

T is the period

So basically the frequency of a wave is the reciprocal of the period.

In this problem, we have

T = 5.47 s is the period of the wave

So, its frequency is

$f=\frac{1}{5.47}=0.183 Hz$

3)

The wavelength of a wave is the distance between two consecutive points with same shape along the wave.

To simplify, the wavelength of a wave can be calculated as the distance between two consecutive crests (or troughs) of the wave, where:

- A crest is the point of maximum (positive) displacement of the wave

- The trough is the point of maximum (negative) displacement of the wave

In this problem, we know that

d = 1.82 m

is the distance between two consecutive crests.

Therefore, the wavelength of the wave is equal to this value:

$\lambda=d = 1.82 m$

4)

The amplitude of a wave is the maximum displacement of the wave measured with respect to the equilibrium position of the wave.

In this problem, we are told that the distance between the highest point and the lowest point on the wave is

d = 0.742 m

This means that this distance is equal to twice the amplitude of the wave, so

d = 2A

where

A is the amplitude of the wave

Therefore, we can solve for A to obtain the amplitude of the wave:

$A=\frac{d}{2}=\frac{0.742}{2}=0.371 m$

5)

The velocity of a wave is given by the so-called wave equation:

$v=f\lambda$

where

v is the velocity

f is the frequency of the wave

$\lambda$ is its wavelength

For the wave in this problem we have:

f = 0.183 Hz is its frequency (found in part 2)

$\lambda=1.82 m$ is the wavelength (found in part 4)

Therefore, the velocity of this wave is:

$v=(0.183)(1.82)=0.333 m/s$