Review Problems: doppler effect and decibels

Like #59

velocity = 20 m/sec
frequency = 600 hz
temperature = 25º C

wave speed = 331 + 0.6(25) = 331 + 15 = 346 m/sec
wavelength = 436 / 600 = 0.575 meters

source moving – change in wavelength

Dl / l = v / v_w
Dl = l * v / v_w
Dl = 0.575 * (20/346)
Dl = 0.033 meters

towards: l’ = l - Dl = 0.575 - 0.033 = 0.542 meters
away: l’ = l + Dl = 0.575 + 0.033 = 0.608 meters

towards: f’ = v_w / l‘ = 346 / 0.542 = 738.4 hz
away: f’ = v_w / l‘ = 346 / 0.608 = 569.1 hz

Like #60

velocity = 20 m/sec
frequency = 600 hz
temperature = 25º C

wave speed = 331 + 0.6(25) = 331 + 15 = 346 m/sec
receiver moving – change in frequency

Df / f = v / v_w
Df = f * (v / v_w)
Df = 600 * (20 / 346)
Df = 34.7 hz

towards: f ‘ = f + Df = 600 + 34.7 = 634.7 hz
away: f ‘ = f - Df = 600 - 34.7 = 565.3 hz

Like #61

f ’ = 520 hz (coming towards)
f ’ = 490 hz (going away)
temperature = 25 ºC

wave speed = 331 + 0.6(25) = 331 + 15 = 346 m/sec
source moving – change in wavelength

towards: l’ = v_w / f ‘ = 346 / 520= 0.665 meters
away: l’ = v_w / f ‘ = 346 / 490 = 0.706 meters

towards: l’ = l - Dl therefore 0.665 = l - Dl
away: l’ = l + Dl therefore 0.706 = l + Dl

adding these two simultaneous equations results in a
value for the source’s wavelength and frequency
1.371 = 2l
0.6855 = l
f = v_w / l = 346 / 0.6855 = 504.7 hz

this allows us to find Dl
0.665 = 0.6855 - Dl
Dl = 0.0205 meters

this in turn allows us to find the velocity of the source
v = v_w* (Dl / l)
v = 346 * (0.0205 / 0.6855 )
v = 10.3 m/sec

Like #29

SL_dB = 10 log ₁₀ (I / I_o)
SL_dB = 10 log ₁₀ (10^-1 / 1 x 10^-12)
SL_dB = 10 log ₁₀ (10¹¹)
SL_dB = 10 x 11
SL_dB = 110 dB

SL_dB = 10 log ₁₀ (I / I_o)
SL_dB = 10 log ₁₀ (10^-6/ 1 x 10^-12)
SL_dB = 10 log ₁₀ (10⁶)
SL_dB = 10 x 6
SL_dB = 6 dB

SL_dB = 10 log ₁₀ (I / I_o)
SL_dB = 10 log ₁₀ (10^-10/ 1 x 10^-12)
SL_dB = 10 log ₁₀ (10²)
SL_dB = 10 x 2
SL_dB = 20 dB

Like #30

SL_dB = 10 log ₁₀ (I / I_o)
75= 10 log ₁₀ (I / 1 x 10^-12)
7.5 = log ₁₀ (I / 1 x 10^-12)
10^7.5 = I / 1 x 10^-12
I = 10^7.5 x 10^-12
I = 3.16 x 10⁷ x 10^-12
I = 3.16 x 10^-5 watts/m²

SL_dB = 10 log ₁₀ (I / I_o)
120= 10 log ₁₀ (I / 1 x 10^-12)
12.0 = log ₁₀ (I / 1 x 10^-12)
10¹² = I / 1 x 10^-12
I = 1 x 10¹² x 10^-12
I = 1 watt/m²