SHOW WORK PLS! Question 1 A string of an instrument is stretched between two poi

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SHOW WORK PLS!

Question 1
A string of an instrument is stretched between two points 25.0 cm apart with a tension of 65.0 N. The mass/length of the string is 4.00x10-3 kg/m. The frequency of the mode of vibration with the lowest frequency (the first harmonic) is:

Given: y(x,t) = (4.3cm)sin[(0.04 rad/cm)x]sin[(40rad/s)t]
276 Hz.
255 Hz.
205 Hz.
182 Hz.

Question 2
A string tied at both ends and oscillating in its 5 harmonic has its shape described by the equation:

What is the length of the string?
25 cm
30 cm
392.5 cm
785 cm

Question 3
The speed of sound in air is 319 m/s. What is the temperature of the air?
-20 degrees C
0 degrees C
20 degrees C
100 degrees C

Question 4
The sound level when one child is talking in a room is 60.0 dB. What would be the sound level if all 20 children talk at the same time in the same room? Assume each child talks equally loudly.
42.4 dB
64.1 dB
73.0 dB
296 dB

Question 5
A wave is described by the equation y = 3sin(5t - 3x + 2?). What is the velocity of the wave?
0.5 m/s
2.0 m/s
1.0 m/s
1.6 m/s

Explanation / Answer

1)here,w = 40 rad/s

or 2pi x f = w

or f = (w/2pi) s^-1

2)the length of string is L = 25 cm

3)we know from the relation

c_air = (331.3 + 0.606 x v) m/s

where v is temperature in oC

here,c_air = 319 m/s

solving the above equation for v

4)the sound level is

L1 = 10 x log(I1/Io) dB

where I1 = 60.0 dB and Io = 10^-12 W/m^2

5)the amplitude of the wave is A = 3 m

the angular frequency is w = 5 rad/s

the maximum speed of the wave is

v_max = A x w = 15 m/s

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