Concept explainers
A guitar string has an overall length of 1.25 m and a total mass of 1.0 g (0.001 kg) before it is strung on the guitar. Once on the guitar, however, there is a distance of 69 cm between its fixed end points. It is tightened to a tension of 74 N.
a. What is the mass per unit of length of this string?
b. What is the wave speed for waves on the tightened string?
c. What is the wavelength of the traveling waves that interfere to form the fundamental standing wave (nodes just at either end) for this string?
d. What is the frequency of the fundamental wave?
e. What are the wavelength and frequency of the next harmonic (with a node in the middle of the string)?
(a)
The mass per unit length of the string.
Answer to Problem 2SP
The mass per unit length of the string is
Explanation of Solution
Given Info: The length of the string is
Write the expression to calculate the mass per unit length of the string.
Here,
L is the length of the string
m is the mass of the string
Substitute
Conclusion:
Therefore, the mass per unit length of the string is
(b)
The wave speed.
Answer to Problem 2SP
The wave speed is
Explanation of Solution
Given Info: The mass per unit length of the string is
Write the formula to calculate the wave speed.
Here,
v is the wave speed
F is the tension on the string
Substitute
Conclusion:
Therefore, the wave speed is
(c)
The wavelength of the travelling wave.
Answer to Problem 2SP
The wavelength is
Explanation of Solution
Given Info: The distance between two end is
Write the expression to calculate the wavelength.
Here,
l is the distance between two ends
Substitute
Conclusion:
Therefore, the wavelength is
(d)
The frequency of the standing wave.
Answer to Problem 2SP
The frequency of the standing wave is
Explanation of Solution
Given Info: The wavelength of the standing wave is The longest possible wavelength is
Write the expression to calculate the speed of the sound wave.
Here,
f is the frequency of the sound wave
Substitute
Conclusion:
Therefore, the frequency of the standing wave is
(e)
The frequency and wavelength of the next harmonic wave.
Answer to Problem 2SP
The frequency of the second harmonic wave is
Explanation of Solution
Given Info: The distance between two end is
Write the formula to calculate the wavelength of the second harmonic.
Here,
Substitute
Write the expression to calculate the speed of the sound wave.
Here,
Substitute
Conclusion:
Therefore, the frequency of the second harmonic wave is
Want to see more full solutions like this?
Chapter 15 Solutions
Physics of Everyday Phenomena
- A sound wave is modeled with the wave function P=1.20Pasin(kx6.28104s1t) and the sound wave travels in air at a speed of v=343.00 m/s. (a) What is the wave number of the sound wave? (b) What is the value for P(3.00 m, 20.00 s)?arrow_forwardA wave traveling on a Slinky® mat is stretched to 4 m takes 2.4 s to travel the length at me Slinky and back again. (a) What is the speed of the wave? (b) Using the same Slinky stretched to the same length, a standing wave is created which consists of three antinodes and four nodes. At what frequency must the Slinky be oscillating?arrow_forwardTwo children stretch a jump rope between them and send wave pulses back and forth on it. The rope is 3 m long, its mass is 0.5 kg, and the force excited on it by the children is 40 N. (a) What is the linear mass density of the rope? (b) What is the speed of the waves on the rope?arrow_forward
- A string on the violin has a length of 23.00 cm and a mass of 0.900 grams. The tension in the string 850.00 N. The temperature in the room is TC=24.00C . The string is plucked and oscillates in the n=9 mode. (a) What is the speed of the wave on the string? (b) What is the wavelength of the sounding wave produced? (c) What is the frequency of the oscillating string? (d) What is the frequency of the sound produced? (e) What is the wavelength of the sound produced?arrow_forward(a) You are driving down the highway in your car when a police car sounding its siren overtakes you and passes you. If its frequency at rest is f0, is the frequency you hear while the car is catching up to you higher or lower than f0? (b) What about the frequency you hear after the car has passed you?arrow_forwardA tunnel under a river is 2.00 km long. (a) At what frequencies can the air in the tunnel resonate? (b) Explain whether it would be good to make a rule against blowing your car horn when you are in the tunnel.arrow_forward
- (a) What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800—Hz sound from its siren? The speed of sound on this day is 345 m/s. (b) What frequency does she receive after the ambulance has passed?arrow_forwardA driver travels northbound on a highway at a speed of 25.0 m/s. A police car, traveling southbound at a speed of 40.0 m/s, approaches with its siren producing sound at a frequency of 2 500 Hz. (a) What frequency does the driver observe as the police car approaches? (b) What frequency does the driver detect after the police car passes him? (c) Repeat parts (a) and (b) for the case when the police car is behind the driver and travels northbound.arrow_forward(a) What is the fundamental frequency of a 0.672—m—long tube, open at both ends, on a day when the speed of sound is 344 m/s? (b) What is the frequency of its second harmonic?arrow_forward
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning