A hiker shouts toward a vertical cliff 789.5m away. The echo is heard 2.1s later. The wavelength of the sound is 12.3 m.
What is the speed of the shout?
What is the frequency?
What is the period of the wave?
To find the speed of the shout, we can use the formula:
Speed = Distance / Time
In this case, the distance is the total path covered by the sound wave, which includes the distance from the hiker to the cliff and back. So, the total distance traveled by the sound wave is 2 times the distance between the hiker and the cliff.
Given:
Distance = 789.5 m
Time = 2.1 s
Let's calculate the speed of the shout:
Speed = (2 * Distance) / Time
= (2 * 789.5 m) / 2.1 s
= 1500 m/s
So, the speed of the shout is 1500 m/s.
Next, let's calculate the frequency:
Frequency is the number of complete wavelengths passing a point per second. The formula for frequency is:
Frequency = Speed / Wavelength
Given:
Speed = 1500 m/s
Wavelength = 12.3 m
Now, let's calculate the frequency:
Frequency = Speed / Wavelength
= 1500 m/s / 12.3 m
≈ 121.95 Hz
So, the frequency of the sound wave is approximately 121.95 Hz.
Lastly, let's calculate the period of the wave. The period is the time taken for one complete cycle or wavelength. The formula for the period is the reciprocal of the frequency:
Period = 1 / Frequency
Given:
Frequency = 121.95 Hz
Now, let's calculate the period:
Period = 1 / Frequency
= 1 / 121.95 Hz
≈ 0.0082 s
So, the period of the wave is approximately 0.0082 s.