Two loudspeakers emit identical sound waves in phase, along the X-axis (see the

Question

Two loudspeakers emit identical sound waves in phase, along the X-axis (see the board). It is found that constructive interference is heard when they are the 20cm apart. As the is speakers are separated it is found that complete destructive interference produced when they are 35cm apart. How long is the wavelength emitted by the speakers? A musician playing a violin, plays a musical note has a wavelength in air of 16.7cm. If the string's linear density is 8.56 Times 10^-4 kg/m and the string is stretched by 200N of tension, how long is the vibrating section of the string?

Explanation / Answer

6)  This a two-step question. First find the frequency from the wavelength and sound velocity, then find the string length from the frequency, linear density and tension.
1. f = c/lambda =344/0.167= 2059.88 Hz
2. From the ref., f = sqrt(T/(m/L))/(2L) ==> L = sqrt(T/(m/L))/(2f) = sqrt(200/8.56*10^-4)/(2*2059.88)

=0.1173m

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