Ch 16: Waves & SoundWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics
What is a Wave?
The Mathematical Description of a Wave
Waves on a String
Wave Interference
Standing Waves
Sound Waves
Standing Sound Waves
Sound Intensity
The Doppler Effect

Concept #1: Standing Waves

Practice: In the following figure, what is the harmonic number of the standing wave? The wavelength of the standing wave? If the frequency of the standing wave is 30 Hz, what is the speed of the waves producing the standing wave?

Example #1: Unknown Harmonic Frequency

Example #2: Standing Wave On A Guitar

Practice: An unknown mass hangs on the end of a 2 m rope anchored to the ceiling when a strong wind causes the rope to vibrate and hum at its fundamental frequency of 100 Hz. If the rope has a mass of 0.15 kg, what is the unknown mass?

Additional Problems
A standing wave is produced with a node at one end and an antinode at the other. If the wave is produced on a string 1.5 cm in length, what is the third-longest wavelength? (a) 6 cm (b) 3 cm (c) 2 cm (d) 1.2 cm
A mass m = 15 kg hangs off the end of a 150 g, 1.2 m string, as shown in the figure below.  (a) What is the fundamental harmonic frequency of the string? (b) What is the first overtone frequency of the string?
A string is stretched to a length ℓ and both ends are fixed. The density of the string is µ and its tension is F. A standing wave mode of the string with six nodes, including both end points (as pictured), is generated. What is the frequency of this oscillation?
A 15 cm string is stretched between two anchor points with a tension of 500 N. If the mass of the string is 170 g, what is the smallest frequency standing wave able to be produced on the string?
Two guitar strings made of the same type of wire have the same length. String 1 has a higher pitch than string 2. Circle all of the correct statements. (a) The wave speed of string 1 is greater than that of string 2. (b) The tension in string 2 is greater than that in string 1. (c) The wavelength of the lowest standing-wave mode on string 2 is longer than that on string 1. (d) The wavelength of the lowest standing-wave mode on string 1 is longer than that on string 2.
Two guitar strings, of equal length and linear density, are tuned such that the second harmonic of the first string has the same frequency as the third harmonic of the second string. The tension of the first string is 600 N. Calculate the tension of the second string.