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Answer :
Final answer:
Using the beat frequency of 2 Hz and given wavelength of 77.3 cm for the piano's tone, the possible frequencies of the violin string are 442 Hz and 438 Hz.
Explanation:
The concept of beat frequency can be used to solve this problem. A beat is the interference between two sound waves with slightly different frequencies, and the beat frequency is equal to the absolute difference between these frequencies. In this question, the beat frequency is 2 Hz, which means the violin's string frequency is either 2 Hz more or 2 Hz less than the piano's frequency. Given the wavelength of 77.3 cm, and using the speed of sound in air at 20°C as 343 m/s, the piano's frequency is calculated as speed of sound / wavelength, equating to about 440 Hz (rounded). Therefore, the possible frequencies of the violin string are 442 Hz (440 + 2) and 438 Hz (440 - 2).
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