UNIT-1:Waves & Vibrations¶

Example no:1.1,Page no:11¶

In :

#Variable declaration
n=512   #frequency in Hz
l=67    #wavelength in cm

#Calculation
v=n*l    #calculating velocity

#Result
print"Velocity = ",v," cm/sec"
print"NOTE:Calculation mistake in book"
Velocity =  34304  cm/sec
NOTE:Calculation mistake in book

Example no:1.2,Page no:11¶

In :

#Variable declaration
v=340   #velocity in m/sec
l=0.68    #wavelength in m

#Calculation
n=v/l    #calculating frequency

#Result
print"Frequency",n,"Hz"
Frequency 500.0 Hz

Example no:1.3,Page no:12¶

In :

#Variable declaration
v=3*10**8   #velocity in m/sec
n=500*10**3    #frequency in Hz

#Calculation
l=v/n    #calculating wavelength

#Result
print"Wavelength=",l,"m"
Wavelength= 600 m

Example no:1.4,Page no:12¶

In :

#Variable declaration
v=330   #velocity in m/sec
n=560.0    #frequency in Hz

#Calculation
lamda=v/n    #calculating wavelength

#Result
print"lambda=",round(lamda,3),"m"
print"Distance travelled in 30 vibrations in m = ",round(lamda*30,2),"m"
lambda= 0.589 m
Distance travelled in 30 vibrations in m =  17.68 m

Example no:1.5,Page no:12¶

In :
import math

#Variable declaration
s=90.0      #distance in m
u=0       #initial velocity in m/sec

#Calculation
t=math.sqrt(90/4.9)     #calculating time using kinematical equation
later=4.56        #Time after which sound is heard
t1=later-t       #calculating time taken by sound to travel
t1=round(t1,2)
v=s/t1       #calculating velocity

#Result
print"Velocity in m/sec = ",round(v,2),"m/s"
Velocity in m/sec =  333.33 m/s

Example no:1.6,Page no:13¶

In :

#Variable declaration
l1=1.5    #wavelength in m
l2=2    #wavelength in m
v1=120   #velocity in m/sec

#Calculation
n=v1/l1     #calculating frequency
v2=n*l2    #calculating velocity

#Result
print"Velocity in m/sec = ",v2,"m/sec"
Velocity in m/sec =  160.0 m/sec

Example no:1.7,Page no:14¶

In :

#Variable declaration
l=5641*10**-10    #wavelength in m
c=3*10**8         #velocity in m/sec
u=1.58        #refractive index of glass

#Calculation
n=c/l          #calculating frequency
cg=c/u         #calculating velocity of light in glass
l1=cg/n       #calculating wavelegth in glass

#Result
print"Wavelength in glass in Angstrom =",l1*10**10,"Angstrom"
print"\n\nNOTE:Calculation ambiguity in book,value of cg is taken as 1.9*10**8 ,Therefore final answer is changed"
Wavelength in glass in Angstrom = 3570.25316456 Angstrom

NOTE:Calculation ambiguity in book,value of cg is taken as 1.9*10**8 ,Therefore final answer is changed

Example no:1.8,Page no:15¶

In :

#Variable declaration
n=12*10**6         #frequency in Hz
v=3*10**8         #velocity in m/sec

#Calculation
l=v/n            #calculating wavelength

#Result
print"Wavelength in m = ",l,"m"
Wavelength in m =  25 m

Example no:1.9,Page no:15¶

In :

#Variable declaration
n=400        #frequency in Hz
v=300.0      #velocity in m/sec

#Calculation
l=v/n            #calculating wavelength

#Result
print"Wavelength=",l,"m"
Wavelength= 0.75 m

Example no:1.10,Page no:22¶

In :
import math

#Variable declaration
a=20       #amplitude in cm
n=6       #frequency per second

#Calculation

#Result
print"y=",a,"sin",round(w,1),"t"
y= 20 sin 37.7 t

Example no:1.11,Page no:23¶

In :

#Variable declaration
a=6      #amplitude in cm
n=9      #frequency in Hz.

#Calculation
vmax=2*(math.pi)*n*6   #calculating velocity in cm/sec
acc=-((18*(math.pi))**2)*6   #calculating acc. in m/sec square

#Result
print"Maximum velocity in cm/sec = ",round(vmax,2),"cm/sec"
print"Velocity at extreme position = 0"
print"Accelaration at mean position = 0"
print"Accelaration at extreme position  = ",round(acc,1),"m/sec^2"
print"\n\nNOTE:Calculation mistake in book"
Maximum velocity in cm/sec =  339.29 cm/sec
Velocity at extreme position = 0
Accelaration at mean position = 0
Accelaration at extreme position  =  -19186.5 m/sec^2

NOTE:Calculation mistake in book

Example no:1.12,Page no:26¶

In :
#Variable declaration
g=9.8    #gravitational constant
m=50    #mass in kg
l=0.2    #length in m
T=0.6     #time period

#Calculation
k=(m*g)/l    #calculating constant
m=2450*((T/(2*(math.pi)))**2)   #calcualting mass using given time period

#Result
print"Mass of body= ",round(m,2),"kg"
print"Weight of suspended body=",round(m,2)*g,"N"
Mass of body=  22.34 kg
Weight of suspended body= 218.932 N