If you set up the seventh harmonic on a string, (a) how many nodes are present, and (b) is there a node, antinode, or some intermediate state at the midpoint? If you next set up the sixth harmonic, (c) is its resonant wavelength longer or shorter than that for the seventh harmonic, and (d) is the resonant frequency higher or lower?
The set up has the seventh harmonic on a string
Determine the number of nodes by knowing the number of harmonics of the standing wave.
Determine the number of nodes for the sixth and seventh harmonic as, for the nth harmonic there are (n+1) nodes. Also, for an even number of harmonics, there is ‘node’ at the midpoint and for the odd number of harmonic; there is ‘antinode’ at the midpoint.
for the nth harmonic, there are (n+1) number of nodes. So, for the seventh harmonic there will be eight nodes.
Hence, for the seventh harmonic, there
For an even number of harmonics, there is ‘node’ at the midpoint and for the odd number of harmonic, there is ‘antinode’ at the midpoint.
So, for the seventh (odd) harmonic, there is an antinode at the midpoint.
Hence, there will be an ‘antinode’ at the midpoint.
Using similar logic of part a), for the sixth harmonic, there are ‘Seven’ nodes.
Hence, for the sixth harmonic, there are ‘seven’ nodes
Applying the same logic of part b), there is a ‘node’ at the midpoint.
Hence, there will be a ‘node’ at the midpoint.
Therefore, determine the number of nodes by knowing the number of harmonics of the standing wave.
A sinusoidal transverse wave of wavelength 20cm travels along a string in the positive direction of an axis. The displacement y of the string particle at x=0 is given in Figure 16-34 as a function of time t. The scale of the vertical axis is set by The wave equation is to be in the form . (a) At t=0, is a plot of y versus x in the shape of a positive sine function or a negative sine function? (b) What is , (c) What is k,(d) What is , (e) What is (f) What is the sign in front of , and (g) What is the speed of the wave? (h) What is the transverse velocity of the particle at x=0 when t=5.0 s?
A standing wave results from the sum of two transverse traveling waves given by and where, x, , and are in meters and t is in seconds. (a) What is the smallest positive value of x that corresponds to a node? Beginning at t=0, what is the value of the (b) first, (c) second, and (d) third time the particle at x=0 has zero velocity?
A sand scorpion can detect the motion of a nearby beetle (its prey) by the waves the motion sends along the sand surface (Figure). The waves are of two types: transverse waves traveling at and longitudinal waves traveling at . If a sudden motion sends out such waves, a scorpion can tell the distance of the beetle from the difference localid="1657274843608" in the arrival times of the waves at its leg nearest the beetle. If localid="1661230422984" , what is the beetle’s distance?
The type of rubber band used inside some baseballs and golf balls obeys Hooke’s law over a wide range of elongation of the band. A segment of this material has an un-stretched length l and a mass m. When a force F is applied, the band stretches an additional length . (a) What is the speed (in terms of m, l , and the spring constant k) of transverse waves on this stretched rubber band? (b) Using your answer to (a), show that the time required for a transverse pulse to travel the length of the rubber band is proportional to if role="math" localid="1660986246683" and is constant if .
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