Question

The Ohio State Marching Band (TBDBITL) is rehearsing for a half time show. They begin by tuning their instruments so that everyone plays with the same pitch. The lead trumpet player sustains an 'A' at 440 Hz. The band members join in one by one and if the new player is off pitch, a beat frequency is heard. (A) The second trumpet player comes in playing slightly out of tune at 443 Hz. What is the beat frequency created when the two play together? (B) Off to the side, the drumline is warming up with a timing drill where all of the bass drummers hit their drum at the same time. If one bass drum is measured to be 78 dB, what is the sound level if all 5 bass drummers play at the same time with the same intensity and the same location (remember to wear hearing protection!)? (C) The band then makes Script Ohio, which is approximately 50 m wide. If the speed of sound is approximately 340 m/s, how long does it take for sound to travel from one side of the band to the other? This can cause the band to get out of sync if they are listening to each other, and not watching the conductor.

Answer 1

(A) Beat frequency :- ( 443 - 440 ) Hz . = 3 Hz.

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(B) Measured sound level of one bass drum = 20 log ( I / I_r ) = 78 dB ................(1)

where I is intensity of sound in W/m² and I_r = 10^-12 W/m² is reference sound intensity .

Hence from eqn.(1) , we get log ( I / I_r ) = 3.9  

I = 10^3.9$\times$ 10^-12 W / m² = 7943 $\times$ 10^-12 W / m²

Intensity of sound due to 5 drums = 5 $\times$ 7943 $\times$ 10^-12 W / m² = 39716 $\times$ 10^-12 W/m²

Sound level in dB for 5 drums = 20 $\times$ log [ ( 39716 $\times$ 10^-12 ) / 10^-12 ] $\approx$ 92 dB

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Time taken for sound to travel 50 m = distance / speed = 50 /340 $\approx$ 0.15 s