Sight and Waves Part 1

Problem Solving

Mr. KlapholzShaker Heights

High School

Problem 1If a pipe is 85 cm long, and open on both ends, what is the lowest frequency standing wave that it can make?Take the speed of sound in air to be 340 m s-1.

Solution 1

Solution 1

For the fundamental, half of a wavelength fits in the pipe.

L = l/2. l = 2L = 2(0.85 m) = 1.7 m

F = v / lF = 340 ms-1 / 1.7m

F = 200 Hz

Problem 2The speed (v) of a wave traveling on a string is given by the expression:

v = { T / m }½ (a) Deduce and expression for the frequency of the fundamental in a string of length L.(b) Use your answer to part (a) to estimate the tension in the ‘A’ string of a violin (frequency = 440 Hz).

Solution 2, part (a)

Imagine the fundamental mode on a string. How does the wavelength compare to the length of the string?l= 2L. f = v / l = {T/m}½ / 2L

Solution 2, part (b)We already know that f = v / l = {T/m}½ / 2L.

T = 4L2mf2 Now we need to estimate the length and the mass

density of the string.L ≈ 0.5 m

m ≈ 2 grams per meter = 2x10-3 kg m-1 T = 4L2mf2 = 4(0.5)2(2x10-3)(440)2

T = 400 N

Problem 3A person in a concert hall is listening to a violin play the note ‘A’ (440 Hz). The violinist is moving toward the listener at 30 m s-1 ! The listener perceives the sound as 484 Hz. What is the speed of sound in the air?

Solution 3

f’ = f × { v / (v ± us) }484= 440 × { v / (v - 30) }

484 (v - 30) = 440v484v –(484)(30) = 440v484v – 440v = (484)(30)

44v = 14520v = 330 m s-1

Problem 4A star is moving away from earth at 3.0 x 105 m s-1. The light emitted from the star has a frequency of 6.0 x 1014 Hz.By how much will the frequency change?

Solution 4

Df’ = f × ( v / c )Df’ = 6.0×1014 × ( 3.0×105 / 3.0×108 )

Df’ = 6.0×1014 × ( 1.0×10-3 )Df’ = 6.0×1011 Hz

This is very small compared to the original frequency.

Problem 4If you shine Red light through a yellow filter, what comes out (if anything)?

Solution 4Red. (The only colors that pass through a Yellow filter are Red and Green.)

Tonight’s HW:

Go through the Sight and Waves section in your textbook and scrutinize the

“Example Questions” and solutions.Bring in your questions to tomorrow’s

class.