1. Lecture 21: Sound Speed of Sound Intensity and Loudness Standing Waves
Doppler Effect
Beats 1

2. Speed of Sound Recall for pulse on string: For fluids:
Speed depends on inertia and restoring force.
For fluids:
Bulk modulus B corresponds to restoring force.
Density r corresponds to inertia.

3. Intensity and Loudness
Intensity is the power per unit area.
I = P / A
Units: Watts/m2
For Sound Waves
I = p02 / (2 r v) (po is the pressure amplitude)
Proportional to p02 (note: Energy goes as A2)
Loudness (Decibels)
Loudness perception is logarithmic
Threshold for hearing I0 = W/m2
b = (10 dB) log10 ( I / I0)
b2 – b1 = (10 dB) log10(I2/I1)

4. Standing Waves Recall for string: For pipe open at both ends:
Node at each end.
Standing wave: ln = 2L/n and v = l f
For pipe open at both ends:
Pressure node at each end. (Pressure there is constant.)

5. Standing Waves For pipe open at one end:
Pressure node at one end; antinode at other end.
Standing wave: ln = 4L/n and v = l f (for n=1,3,5…)

6. Doppler Effect When source is moving toward you:
Distance between waves decreases
Frequency increases
When source is moving away from you:
Distance between waves increases
Frequency decreases
When moving toward source:
Velocity of waves increases
When moving away from source:
Velocity of waves decreases

7. Beats + Consider two harmonic waves A and B meeting at x=0.
Same amplitudes, but different frequencies.
Their superposition (sum) is shown below:
A(t) +
B(t)
C(t)
CONSTRUCTIVE INTERFERENCE
DESTRUCTIVE INTERFERENCE
Beat Frequency = | f1 – f2 | = f

8. Summary Speed of sound: Intensity: B = (10 dB) log10 ( I / I0)
Standing Waves
Open at both ends: ln = 2L/n (n=1,2,3…)
Open at one end: ln = 4L/n (n=1,3,5…)
Doppler Effect:

9. Example
Your “friend” plays a note on his saxophone (middle C, frequency 262 Hz). Knowing how bad of a saxophone player he is you begin riding your bike away from him at 8 m/s. However, he gets in his car and drives toward you at 26 m/s (playing the saxophone the whole time). What frequency do you hear as your “friend” chases you? (Assume the speed of sound is 343 m/s.)
We will use the Doppler Effect Equation:

10. Example
Your “friend” plays a note on his saxophone (middle C, frequency 262 Hz). Knowing how bad of a saxophone player he is you begin riding your bike away from him at 8 m/s. However, he gets in his car and drives toward you at 26 m/s (playing the saxophone the whole time). What frequency do you hear as your “friend” chases you? (Assume the speed of sound is 343 m/s.)
Solve for fo:
= 277 Hz
(the note C#)