Sound Review

True or False?

• 1. The transverse waves on a vibrating string are different from sound waves.

• 2. Sound waves are longitudinal pressure waves.

• 3. Light travels very much slower than sound.

• 4. Sound can travel through vacuum.

• 5. "Pitch" (in music) and frequency have approximately the same meaning.

• 6. Decibels are related to sound intensity.

What are beat frequencies?

• The difference in pitch between 2 frequencies. (No beats indicate the frequencies are the same.)

• fb = f1 – f2 • Example: If two piano strings had

frequencies of 529 Hz and 534 Hz what would the beat frequency be?

• 534 – 529 = 5 Hz

Another example:

• What if a 346 tone is played and a beat frequency of 4 Hz is heard. What is the frequency of the other tone?

• Either 350 or 342 Hz.

What do decibels measure?

• Intensity level (loudness).

• A sound twice as loud has 10 times the intensity.

• A log scale is used. β = 10dB log (I/Io)

• Difference in the decibel levels of the two sounds is β = 10dB log (I2/I1)

How is intensity measured? • I = P/A

• At a distance of 3.8 m from a siren, the sound intensity is 3.6 x 10-2 W/m2. Assuming that the siren radiates sound uniformly in all directions, find the total power radiated.

• P = 4πr2I = Energy/time • P = 6.5 W

Linear Density

• A uniform wire carries waves whose frequency and wavelength are 450Hz and 1.2 m respectively. If the string is known to be under a tension of 250 N, what is the linear density of the wire?

• Use m/L = F/v2.

• V is found using v = λf, v=540 m/s, so

• μ = m/L = 8.57 x 10-4 kg/m.

Some Vocabulary• Mach?• Faster than the speed of sound• Doppler?• Change in frequency due to motion of the source or

observer.• Superposition?• Sound is the sum of all the sound waves.• Interference?• Constructive and Destructive• Ultrasound?• Outside upper range of human hearing.

Superposition/Interference• Two pulses of identical shape travel toward each other in

opposite direction on a string as shown in the figure.

• Which one of the following statements concerning this situation is true?

• A) The pulses will reflect from each other. • B) The pulses will interfere to produce a standing wave. • C) The pulses will pass through each other and produce

beats. • D) As the pulses pass through each other they will cancel

each other out.

• Examples of an Open Pipe?

• Trumpet, trombone, sax, flute

• Closed pipe?

• Organ

Harmonics – f1, f2, f3…

• What’s the fundamental frequency?• f1

• Which have all harmonics?• Open/open and fixed string• Which have only odd?• Open/closed• Which have only even?• None

Example:

• If f1 is 260 Hz, what is f2?

• 520 Hz

• f3?

• 780 Hz

• f4?

• 1040 Hz

The lowest note one type of flute can produce with all the holes

closed is a “C” note with a fundamental frequency of

261.6Hz. Flutes are an open tube. How long should the distance be from the mouthpiece to the end to

make this sound? Use v = 343 m/s

Solution • Use n = 1

• f = v/(2L). L = ?

• L = v/(2f1)

• L = 0.656 m

• What L is needed if temp changes, so that the velocity of sound = 350 m/s?

• Now L = 0.669 m

The fifth harmonic of standing waves in a pipe closed at one end is 512 Hz. How long is the pipe? Use

v = 343 m/s.

• f5 = 5v/4L,

• L = 0.84 m

A piano string is 1.10 m long. If it supports a fundamental frequency with a velocity of 288 m/s, what would be the wavelength? What is the fundamental frequency? The

second, third and fourth harmonics?

• Wavelength is 2.2 m,

• f1= 131 Hz, f2 = 262, f3 = 393, f4 = 524 Hz

Draw the standing wave patterns. Label the nodes and antinodes.

For a string with both ends fixed

Organ Pipes Open at both ends

Organ Pipe with one end closed

A train is traveling at 44.7 m/s when the engineer sounds a warning horn at 415 Hz. The speed of sound is 343 m/s. What are the frequencies and wavelengths heard by a person standing at the crossing as the train approaches and leaves?

Approaches: f = 477 Hz λ =0.719m

leaves, f = 367 λ = 0.935

If a police car emits sounds its horn (250 Hz) while stationary, what frequency would be heard

by an observer approaching it at 27 m/s (60 mph)? Use v = 340 m/s.

270 Hz