1. Sound Worksheet 2 Answers 1. A train emits a constant signal of 500 Hz as it approaches a crossing at 25.0 m/s on a 10.0 o C day. A car waits at the crossing. (a) What frequency does the driver hear as the train approaches the crossing? Approachf’ = f s v v – v s ( ) f’ = ?f s = 500 Hzv s = 25 m/s v = 331.4 m/s + ( 0.6 )( 10 ) = 337.4 m/s 337.4 337.4 - 25 = ( 500 Hz ) = ( 500 Hz )( 1.08 ) f’ = 540 Hz ( )

2. 1. A train emits a constant signal of 500 Hz as it approaches a crossing at 25.0 m/s on a 10.0 o C day. A car waits at the crossing. (b) What frequency does the driver hear as the train recedes from the crossing? Recessionf’ = f s v v + v s ( ) f’ = ?f s = 500 Hzv s = 25 m/s v = 331.4 m/s + ( 0.6 )( 10 ) = 337.4 m/s 337.4 337.4 + 25 = ( 500 Hz ) = ( 500 Hz )( 0.931 ) f’ = 466 Hz ( )

3. 1. A train emits a constant signal of 500 Hz as it approaches a crossing at 25.0 m/s on a 10.0 o C day. A car waits at the crossing. (c) What frequency does the conductor hear? No relative motion between the train and the conductor f’ = 500 Hz

4. 2. A wire 1.80 m long is stretched between two clamps. Waves travel with a speed of 250 m/s through the wire. (a) A standing wave is formed that has two nodes and three antinodes. Draw the standing wave. 1.80 m

5. λ = 2 / 3 L 2. A wire 1.80 m long is stretched between two clamps. Waves travel with a speed of 250 m/s through the wire. (b) What is the wavelength of the traveling wave that would form this standing wave? 1.80 m = 2 / 3 ( 1.80 m ) λ = 1.20 m

6. 2. A wire 1.80 m long is stretched between two clamps. Waves travel with a speed of 250 m/s through the wire. 1.80 m (c) The wave formed is the ( fundamental, 2 nd harmonic, 3 rd harmonic )

7. 3. A wire 2.00 m long is clamped at both ends. (a) What is the wavelength of the fundamental? 2.00 m λ = 2 L= 2 ( 2.00 m ) λ = 4.00 m

8. 3. A wire 2.00 m long is clamped at both ends. (b) If waves travel down the wire at 240.0 m/s, what is the fundamental frequency? λ f = 4.00 m 2.00 m v = f λ λ f = v λ = 240 m/s 4.00 m f = 60 Hz

9. 3. A wire 2.00 m long is clamped at both ends. (c) What is the frequency of the sound wave produced? λ f = 4.00 m f f = 60 Hz 2.00 m The wire vibrates 60 times per second, creating 60 compressions per second f = 60 Hz Once a wave is generated, it never changes frequency, even when it goes into different media

10. 3. A wire 2.00 m long is clamped at both ends. (d) What is the frequency of the third harmonic? f 3 = 3f f 3 = 180 Hz