Answer all problems: Solution are provided, I need the step by step solutions. T

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Answer all problems: Solution are provided, I need the step by step solutions.

The displacement of a wave traveling in the positive x direction is y(x, t) = (3.5 cm)cos (2.7x + 92t), where x is in m and t is in seconds. What are the Frequency (15 Hz) Wavelength (2.3 m) Speed of this wave? (35 m/s) The snapshot graph of a wave at t = 0 s is shown below. What are the amplitude, wavelength and frequency of the wave? (4 cm, 12m and 2.0 Hz) A rock band playing an outdoor concert produces sound at 120 dB 5.0 m away from their single working loudspeaker. What is the sound intensity level 35 m from the speaker? (103 dB) A loud speaker produces sound of sound level (loudness) 120 dB at some distance. What would be the loudness if there were 20 such identical speakers at the same distance? (133 dB) Standing in a certain location, Poindexter hears the distinctive call of a single Bob White Quail (Colinus virginianus) off in the distance. He measures the sound level from this quail to be 58 dB. What sound level would Poindexter measure at his location if there were a dozen similar Bob White Quail each calling with the same average power and all gathered in the same location as the lone quail? (68.8 dB) A friend of yours is loudly singing a single note at 400 Hz while driving toward you at 25.0 m/s on a day when the speed of sound is 340 m/s. What frequency do you (at rest) hear? (431 Hz) What frequency does your friend hear if you suddenly start singing at 400 Hz? (429 Hz)

Explanation / Answer

16)

wave Equation is

y(x,t) = A*cos(kx+wt)

we have ,

y(x,t) = (3.5cm)*cos(2.7x+92t)

so,

w = 92 rad/s, k = 2.7 N/m

a)

frequency = w/(2*pi) = 92/(2*pi) = 14.64 Hz = 15 Hz

b)

Wavelength = 2*pi/k = 2*pi/2.7 = 2.3 m

c)

speed = frequency*wavelength = 15*2.3 = 34.5 m/s

17)

Amplitude = max. displacement = 4 cm

Wavelength = distance b/w two consecutive crest = 12 m

frequecy = speed/wavelength = 24/12 = 2 Hz

18)

L1 = 10*log(I1/(10^-12) dB = 120 dB

so,

I1= 10^(L/10)*(10^-12) = 10^(120/10)*(10^-12) = 1

I2 = I1*r1^2/r2^2 = 1*5^2/35^2 = 0.02

L2 = 10*log(I2/(10^-12) = 10*log(0.02/(10^-12) = 103 dB

19)

I1 = 10^(L1/10)*(10^-12) = 10^(120/10)*(10^-12) = 1

so,

I2 = 20*I1 = 20

so,

L2 = 10*log(I2/(10^-12) = 10*log(5/(10^-12) = 133 dB

20)

I1 = 10^(L1/10)*(10^-12) = 10^(58/10)*(10^-12) = 6.3*10^-7

so,

I2 = 12*I1 = 12*6.3*10^-7 = 0.00000756

so,

L2 = 10*log(I2/(10^-12) = 10*log(0.00000756/(10^-12) = 68.8 dB

21)

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