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Waves

Q- Earthquakes are essentially sound waves traveling through the earth. They are called seismic waves. Because the earth is solid, it can support both longitudinal and transverse seismic waves. These travel at different speeds. The speed of longitudinal waves, called P waves, is 8000 m/s. Transverse…

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Sound Waves: Interference

Q- A riverside warehouse has two open doors and its walls are lined with sound absorbing material. A boat on the river sounds its horn. To a person A on the perpendicular bisector of the doors, at a distance 150 m from the doors, sound is loud and clear while to a person B, 30 m sideways from A, the…

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Waves on string

Q- An apparatus similar to the one used in lab uses an oscillating motor at one end to vibrate a long rope with frequency f = 35 Hz and amplitude A = 0.25 m. The rope is held at constant tension by hanging a mass on the other end. The length of the rope is adjusted to form loops.The rope has mass de…

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Standing Waves

Q- What are the three longest wavelengths for standing sound waves in a 121 cm long tube that is

(a) open at both ends

(b) Open at one end and closed at the other.

Solution:

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Wave Motion

Q- In the oceans, whales communicate by sound transmission through the water. A whale emits a sound of 60 Hz to tell a wayward calf to catch up to the pod. The speed of sound in water is about 1500 m/s.

(a) How long does it take the sound to reach the calf if he is 1.46 km away?

(b) What is the wa…

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Sound Waves

Q- Figure shows a snapshot graph at t = 0 s of a 30.0 Hz wave traveling to the left. Each interval on the vertical axis corresponds to 5 mm. 

(a) What is the wave speed?

(b) What is the phase constant of the wave?

(c) Write the displacement equation for this wave.

Solution:

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Wave Motion

Q- The displacement of a wave traveling in the negative y-direction is D(y, t) = (5.0 cm) sin (5.5y + 74t) where y is in m and t is in s. What are each of the following for this wave?

(a) Frequency

(b) Wavelength

(c) Speed

Solution:

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Sound Waves: Doppler Effect And Beats

Q- A trumpet player is on a flatcar drawn by a locomotive and another player is near tracks. If each player blows a 440 Hz note, and if there are 4 beats/s as they approach each other, what is the speed of the flatcar? (Speed of sound in air is 340 m/s)

Solution:

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Sound: Shock Cone

Q- A person looks directly overhead and sees a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time he hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km.

(a) Find the angle of the shock cone.

(b) Find the speed of the plane (the Mach nu…

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Standing Waves

Q- A steel wire having a mass of 5 g and a length of 1.2 m is fixed at both ends and has a tension of 974 N.

(a) Find the speed of transverse waves on the wire.

(b) Find the wavelength of the fundamental.

(c) Find the frequency of the fundamental.

(d) Find the frequency of the second harmonic.

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Standing Waves: Air column

Q- The normal range of hearing is about 20 to 20000 Hz. Assume that your hearing range is 27 to 18500 Hz. (Use 340 m/s as the speed of sound.)

(a) What is the greatest length of an organ pipe that would have its fundamental note in your hearing range if it is closed at one end?

(b) What is the gre…

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Wave Equation

Q- A wave on a string is described by D(x,t) = (3.0 cm) sin[2π(1 + x/(2.1 m) - t/(0.2 s))].

(a) In what direction is this wave traveling?

(b) What are the wave speed, the frequency, and the wave number?

(c) At t = 0.50 s, what is the displacement of the string at x = 0.20 m?

Solution:

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Interference (sound)

Q- Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 22 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 66 cm.

(a) What is the wavelength of the sound?
(b) If the d…

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Standing Waves on String

Q- The G string on an instrument is 49 cm long. When played without fingering, it vibrates at a frequency of 196 Hz. The next higher notes on the C-major scale are A (220 Hz), B (247 Hz), C (262 Hz), and D (294 Hz). What distance x from the end of the string must a finger be placed to play each of t…

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Standing waves: Resonance

Q- A shower stall measures 86.0 cm x 86.0 cm x 210cm long. When you sing in the shower, which frequencies will sound the richest (because of resonance)? Assume the stall acts as a pipe closed on both ends, with nodes at opposite sides. Assume also that the voices of various singers range from 130 Hz…

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Standing Wave on String

Q- A uniform string of linear density 10g/m is tied to the ceiling of an elevator. A 5kg mass is hung from the other end of the string at a point 1m from the ceiling. If the elevator accelerates upward at 0.10g what is the fundamental frequency of the string?

Solution:

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Loudness

Q- A person standing a certain distance from an airplane with four equally noisy jet engines experiences a sound level of 120dB. What sound level intensity would this person experience at double the initial distance when the captain shuts down all but one engine?

Solution:

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Interference (sound)

Q- Your friend Ram wants to talk to you. You both are 12 meters apart. A long wall is located 8 meters to the side of both. When Ram talks, you hears the sound coming directly from Ram, and the sound that reflects off the wall. What is the lowest frequency that Ram should talk so that when the two w…

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Waves

Q- Two waves traveling in same direction are present at a point in space have amplitudes d1(t)=4sin(wt) and d2(t)=4cos(wt). Determine the resultant amplitude at that point.

Solution:

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Standing Wave on String

Q1- Standing waves of frequency 180 Hz are produced on a string of length 60 cm and it vibrates making three loops. What is the wave speed on the string?  

Q2- A 121 cm long string with mass 4.0 g oscillates in its m=3 mode with a frequency of 180 Hz and a maximum amplitude of 5.0 mm. What are (a)…

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