course phy201
The SHM of the left-hand end of a long string is given by y=1.84cm*sin((7`pi rad/s)t). This motion induces a traveling wave in the string. The string has tension 33N and `mu 15g/m. Find how much energy there is in 13m of this wave.
2`pi*f=7`pi, so f=7/2 Hz. mass in 13m=.015*13=.195kg. v(max)=2*`pi*A*f=2*`pi*.0184*(7/2)=.405m/s, so E=.5*.195*.405^2=.016J.
Traveling waves are set up in a pair of long strings by a single harmonic oscillator. The waves have identical propagation velocities of 160m/s. Both strings terminate at a short bungee cord attached to a wall. The harmonic oscillator is attached to the other ends of the strings in such a way that one string is 5.9m longer than the other. Give at least 2 oscillation frequencies which will produce the max motion of the bungee cord and 2 which will produce the min motion.
The max motion occurs when the wavelength equals 5.9m or a whole integer multiple of it. So, 160/5.9=27.1 Hz and 160/(2*5.9)=13.6 Hz. The min motion occurs when the wavelength equals (.5+5.9) or a whole integer multiple of it. So, 160/(.5+5.9)=25 Hz and 160/(2*(.5+5.9))=12.5 Hz.
Be careful here and be sure you visualize the situation to be sure you have the relationships right.
Reinforcement occurs when the additional length of the string is a whole number of wavelengths; this occurs when the wavelength is equal to the length of the string divided by (not multiplied by) a whole number.
Destructive interference occurs when the additional length of the string is a whole number plus half a wavelength. THis occurs when the wavelength is equal to the length of the string divided by a whole number plus .5.
At clock time t the y position of the left-hand end of a long string is y=1.53cm * sin ((4`pi rad/s) t). The string extends along the x axis, with the origin at the left end of the string, which is held under tension 39N and has mass per unit length 9g/m. The motion of the left end creates a traveling wave in the string. Find the equation for the y displacement a point 17.2m down the string as a function of clock time. If the position of the left-hand side is x=0, find the equation for the y displacement as a function of clock time at arbitrary position x.
v=`sqrt(39/.009)=65.8m/s. at 17.2m down the string, y=1.53cm * sin ((4`pi rad/s) (t-(17.2/65.8)). at arbitrary x, y=1.53cm * sin ((4`pi rad/s) (t-(x/65.8)).
Good work, but be sure you have the reasoning straight on how many waves fit into the additional path length (as opposed to how many times the additional path length fits into a wave).
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