Question
Link and Zelda are at the beach. Link is standing on the shore and Zelda is doing some underwater swimming. They both hear a boat that is 3,200 m (2 miles) away. They are both able to measure the frequency and wavelength of the sound wave they hear. What is a possible frequency and wavelength that Zelda could report? It is a very sunny day and both the water and air are at 20 degrees Celsius.
A possible frequency and wavelength that Zelda could report can be calculated using the speed of sound in water and air. The speed of sound in water at 20 degrees Celsius is approximately 1,483 m/s, and in air at the same temperature is approximately 343 m/s.
Given that the boat is 3,200 m away, the sound wave must travel through both water and air to reach Zelda. Let's assume the sound wave first travels through water and then air.
Let's calculate the time it takes for the sound wave to travel through water and air to reach Zelda:
Time taken to travel through water = Distance / Speed = 3,200 m / 1,483 m/s ≈ 2.16 seconds
Time taken to travel through air = Distance / Speed = 3,200 m / 343 m/s ≈ 9.34 s
Total time taken = Time in water + Time in air = 2.16 s + 9.34 s = 11.50 s
Now, let's calculate the frequency and wavelength that Zelda could report:
Frequency = 1 / Total time taken = 1 / 11.50 s ≈ 0.087 Hz
Wavelength in water = Speed in water / Frequency = 1,483 m/s / 0.087 Hz ≈ 17,052 m
Wavelength in air = Speed in air / Frequency = 343 m/s / 0.087 Hz ≈ 3,948 m
Therefore, a possible frequency that Zelda could report is approximately 0.087 Hz, with a wavelength of 17,052 m in water and 3,948 m in air.
Zelda and Link would report the same amounts because sound waves are always the same
Zelda and Link would report the same amounts because sound waves are always the same
Zelda reports a frequency of 10 Hz and a wavelength of 50 m
Zelda reports a frequency of 10 Hz and a wavelength of 50 m
Zelda reports a frequency of 12 Hz and a wavelength of 28.6 m
Zelda reports a frequency of 12 Hz and a wavelength of 28.6 m
Zelda reports a frequency of 12 Hz and a wavelength of 123.5 m
Zelda and Link would report the same amounts because sound waves are always the same.
Therefore, if Zelda reports a frequency of 12 Hz and a wavelength of 123.5 m, Link would also report the same frequency and wavelength since sound waves are consistent given the same conditions.