Question

s] From a distance of ra = 8.000 m, a trumpet player plays an A note, f1 = 440.0 Hz, with a sound intensity level of β1 = 58.00 dB. A tuba plays in unison with the trumpet, but is slightly out of tune and has f2 = 437.00 Hz, and its sound intensity level is β2 = 63.50 dB. a) Calculate I1 and I2, the intensities of each instrument separately. b) When they play in unison, how many decibels does their combined sound create? c) What beat frequency is heard? d) If the distance to the instruments is increased to rb = 24.00 m, what are the sound intensity levels (in dB) of the trumpet by itself, the tuba by itself, and the combined instruments?

Answer 1

(a)

1 = 10 log ( I1 / Io)

58 = 10 log ( I1 / 1e-12)

1058/10 = I1 / 1e-12

I1 = 6.3095e-7 W/m2

and

2 = 10 log ( I2/ Io)

63.5 = 10 log ( I2/ Io)

I2 = 2.238e-6 W/m2

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(b)

Total level

= 10 log ( 105.8 + 106.35 )

= 64.578 dB

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(c)

beat frequency = 440 - 437 = 3 Hz

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(d)

Intensity power / area

6.3095e-7 = P / 482

P = 5.074e-4 W

so,

at r = 24 m

I = 7.01e-8 W/m2

so,

1 = 48.45 dB

and

for second instrument

2.238e-6 = P /482

P = 1.7999e-3 W

so

at r = 24 m

I = 2.487e-7 W/m2

so,

2 = 53.95 dB

and

combined level is

= 55.028 dB