Question

A hiker shouts toward a vertical cliff 481 m away. The echo is heard 3.0 s later. The wavelength of the sound is 0.9 m. What is the frequency?
Group of answer choices

541 Hz

1,671 Hz

357 Hz

1,357 Hz

Answer 1

To find the frequency of the sound, we first need to determine the speed of sound using the time it takes for the echo to return.

1. **Calculate the total distance the sound travels:**
Since the hiker is shouting towards a cliff and waiting for the echo to come back, the sound travels to the cliff and then back to the hiker. Thus, the total distance traveled by the sound is:
\[
\text{Total Distance} = 2 \times \text{Distance to Cliff} = 2 \times 481 \, \text{m} = 962 \, \text{m}
\]

2. **Determine the speed of sound:**
The total time for the echo to return is 3.0 seconds. Therefore, the speed of sound can be calculated as:
\[
\text{Speed of Sound} = \frac{\text{Total Distance}}{\text{Time}} = \frac{962 \, \text{m}}{3.0 \, \text{s}} \approx 320.67 \, \text{m/s}
\]

3. **Calculate the frequency using the relationship between speed, frequency, and wavelength:**
The formula relating speed (v), frequency (f), and wavelength (λ) is:
\[
v = f \times \lambda
\]
Rearranging for frequency gives:
\[
f = \frac{v}{\lambda}
\]
Substituting the calculated values into this equation:
\[
f = \frac{320.67 \, \text{m/s}}{0.9 \, \text{m}} \approx 356.3 \, \text{Hz}
\]

4. **Select the closest answer choice:**
The closest answer to 356.3 Hz in the provided options is **357 Hz**.

Therefore, the frequency of the sound is approximately **357 Hz**.