Physics Question & Answer Key

Question:

When two organ pipes open at both ends are sounded at their first harmonic, 4 beats/second are heard. One pipe is 1000 mm long. Calculate the length of the other pipe.

Answer:

V = 343 m/s

L₁ = 1000 mm = 1 m

λ = 2L₁ = 2 m

f_beat = ½f₁ – f₂½

4 = (343 / 2) – (343 / l₂)

λ₂ = 2.048

λ₂ = 2L₂

2.048 = 2 L₂

L₂ = 1.024 m = 1024 mm

Physics Question & Answer Key

Question:

A vibrating string on a violin is 330 mm long and has a fundamental frequency of 659 Hz. Tge string is then pressed on against the fingerboard at a point of 60 mm from its end.
a) Calculate the fundamental frequency when the string is pressed against the fingerboard. 
b) Calculate the wavelength of the sound wave produced. 
c) Calculate the frequency of the next two harmonics. 


Answer:

f = 659 Hz
L = 0.33 m
L_{1 = 0.33 - 0.06 = 0.27 m}

a) 

v = λf
   = (659)(2)(0.33)
   = 434.94 m/s

f_{1= (434.94) / (2)(0.27)}

   _{= 805 Hz}

_b) 

λ = v / f
   = (343) / (805)
   = 0.43 m

c)

f_{2 = (2)(434.94) / (2)(0.27)}

    _{= 1611 Hz}

f_{3 = (3)(434.94) / (2)(0.27)}

    _{= 2416 Hz}

Physics Questions & Answer Key

Question:

Mr. Physics drops a rock down a 250-meter deep well. Upon impact with the bottom of the well a short burst of sound is produced with a frequency of 250 Hz. How much time after he drops the rock does he hear it hit the bottom of the well.


Answer:

d = 250 m

f = 250 Hz

v = 343 m/s

u = 0 m/s

d = ut + ½ gt²

250 = (0)(t) + ½(9.8)( t²⁾

t = 7.143 sec  (going down well)

d = vt

250 = (343)(t)

t = 0.729 sec (going back up well)

t = 7.143 + 0.729 = 7.872 sec

  

Physics Question & Answer Key

Question:

Two identical ice skaters are holding onto opposite ends of a very long spring with 

a spring constant of 650 N/m. While spinning in a circle, the skaters frequency of 

revolution is measured to be 0.85 Hz. Calculate the mass of the skaters. 


Answer:

f = (1/2 π)(√ k/m)

0.85 = (1/2 π)(√ 650/m)  

m = 22.8 kg 

22.8 x 2 = 45.6 kg  (the mass need to double since circular motion is the resultant 

of two perpendicular SHM with the same frequency and amplitude and phase 

difference of π/2.)

Physics Question & Answer Key

Question:

A car traveling at constant speed negotiates a frictionless banked curved. Calculate the speed of the car when the road is banked at 20 degrees and the radius of its path is 50 meters.

Answer:

When the road is banked at angle 20 degrees,
The normal force is inclined at angle 20 degrees to the vertical
Its horizontal component
mg sin 20 = centripetal force = mv^2/r
Its vertical Component balances the weight 
mg cos 20 = mg 
Dividing the first by the second equation
tan 20 = v^2/(rg)
v^2 / 50 = (9.8)(tan 20)
v = 13.35 m/s