# 3 Problems involving superposition

by mst3kjunkie
Tags: involving, superposition
P: 16
Here are the three problems I'm having trouble with:

 1. The problem statement, all variables and given/known data Two identical loudspeakers separated by distance d emit 170 Hz sound waves along the x-axis. As you walk along the axis, away from the speakers, you don't hear anything even though both speakers are on. What are three possible values for d? Assume a sound speed of 340 m/s. 2. Relevant equations phase difference = 2*Pi*(change in r/wavelength)+initial phase difference=2(m+1/2)Pi interference is destructive if the path-length difference r=(m+1/2)wavelength 3. The attempt at a solution find the wavelength f=v/2L = v/wavelength wavelength=v/f =340/170 =2 d=(m+1/2)wavelength for m=0: d=1m m=1: d=2m m=2 d=3m did I do this correctly?
 1. The problem statement, all variables and given/known data A steel wire is used to stretch a spring. An oscillating magnetic field drives the steel wire back and forth. A standing wave with three antinodes is created when the spring is stretched 8.0cm. What stretch of the spring produces a standing wave with two antinodes 2. Relevant equations unsure 3. The attempt at a solution the wave is in the third harmonic. The wavelength can be found using wavelength=4L/m =4(.08)/3 = 8/75 I'm not sure how to get to the book's answer of 18 cm.
 1. The problem statement, all variables and given/known data Two loudspeakers 5.0m apart are playing the same frequency. If you stand 12.0 m in from of the plane of the speakers, centered between them, you hear a sound of maximum intensity. As you walk parallel to the plane of the speakers, staying 12.0m in front of them, you first hear a minimum of sound intensity when you are directly in from of one of the speakers. a. what is the frequency of the sound? Assume a sound speed of 340 m/s b. If you stay 12.0m in front of one of the speakers, for what other frequencies between 100 Hz and 1000 Hz is there a minimum sound intensity at this point? 2. Relevant equations unsure for part b 3. The attempt at a solution I've solved part a, f=170 Hz. I don't even know how to start part b.
HW Helper
P: 1,772
First problem:
 Quote by mst3kjunkie 3. The attempt at a solution find the wavelength f=v/2L = v/wavelength wavelength=v/f =340/170 =2 d=(m+1/2)wavelength for m=0: d=1m m=1: d=2m m=2 d=3m did I do this correctly?
Excessive busywork led you to the correct final equation, then you did the simple math wrong. plug in your m's again.
 P: 102 3 Problems involving superposition Isn't the $$\lambda$$ for the third harmonic $$\frac{2L}{3}$$? If you use hookes law, don't we need to know the spring constant k before using this information to solve this problem?