course Phy 202
I have a few questions -- Again from Test 2
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The SHM of the left-hand end of a long string is given by y = .98cm * sin(4pirad/s)t). This motion induces a traveling wave in the string. The string has tension 15 Newtons and mass per unit length is 14 grams/meter. What is the equation for the SHM of a point 4.5 meters down the string?
I worked this part out from our in-class analysis:
y(4.5,t)=.98sin (4 'pi t-2'pi/34.7 * x)
and using 4.5 for x I got,
... =.98cm sin (4'pi t-2'pi/34.7 * 4.5) = y(4.5,t)=.98cm sin(4'pi t-9 pi/34.7)
The second part to this problem says
If the position of the left-hand side is x=0, what is the equation for the SHM at arbitrary postion x?
When I use 0 for x then I get y(0,t)=.98cm sin(4'pi t-2'pi/34.7 * 0) = .98 cm sin (4'pi t).
Is this correct? When I use 0 for x it cancels out the second part of the equation.
x = 0 is a specific, not an arbitrary position.
'Arbitrary position x' means that you use the symbol x for the position and give the equation in terms of x and t.
The correct answer here is just the function .98sin (4 'pi t-2'pi/34.7 * x), which you gave previously.
I think I worked this problem correctly -- What is the fundamental frequency of a longitudinal standing wave in an aluminum rod of length 7 meters, balanced at its midpoint, if a longitudinal disturbance travels at 5000 m/s? My answer -- 1/2 lambda = 7m, so lambda = 14m, Vprop =5000m/s. Period is 14m/5000m/s=.0028 sec, Frequency = 1/.0028 sec = 357.14 Hz. Is my analysis correct?
This is correct.
And finally we went over decibels in class but I am a little confused on Intensity. The problem reads One sound is 7500 times louder than a sound which measures 45 decibels. What is the decibel level of this sound? If I take 45 dB and multiply that by 7500, is this intensity? I understand how to use dB=10 log (I/Io) but am not sure how to determine Intensity for this problem.
I is the intensity. To get I you have to solve the equation for I:
log(I / I0) = dB / 10 so
I / I0 = 10^(dB/10) and
I = I0 * 10^(dB/10).