Question

What is the wavelength of sound generated by a 2m piano string in its normal mode of vibration? Piano strings are heavy (699 g) and under high tension, 90 kN. Express your answer in meters.

(a) 0.0012 m
(b) 0.0024 m
(c) 0.0036 m
(d) 0.0048 m

Answer 1

To find the wavelength of the sound created by the piano string, you must first calculate the speed of waves on the string using the tension and the mass density. Then, since the string's normal mode has a wavelength twice its length, you can find the desired wavelength. Option D is correct.

Step-by-step explanation:

The question is about finding the wavelength of sound generated by a 2 meter piano string vibrating in its normal mode. The key to solving this problem lies in using the properties of standing waves on strings and knowing the formula for wave speed as well as the relationship between speed, frequency, and wavelength of a wave.

To find the wavelength (λ), you must first determine the speed of the wave (v) on the string using the formula:
v = √(T/μ), where T is the tension and μ is the linear mass density.

Once we have the speed, we can use the fact that in the normal mode of vibration, the length of the string (L) is half the wavelength (L = λ / 2), since there is one antinode in the middle of the string and two nodes at its ends. Rearranging this relationship gives us λ = 2L.