#importing modules
import math
from __future__ import division
#Variable declaration
E=80*10**9; #Young's modulus of material of piezo electric crystal(Pa)
d=2654; #Density of material of piezo electric crystal(Kg/m^3)
t=0.1*10**-2; #Thickness of piezo electric crystal(m)
p=1; #for fundamental first overtone
#Calculation
f=((p/(2*t))*(math.sqrt(E/d))); #Frequency of vibration of first overtone(Hz)
#Result
print "The frequency of vibration is",round(f/10**6,4),"*10**6 Hz"
#importing modules
import math
from __future__ import division
#Variable declaration
v=5.5*10**3; #Velocity of longitudanal waves in Quartz Crystal(m/s)
t=0.05; #Thickness of Quartz Crystal(m)
#Calculation
w=2*t; #wavelength(m)
v1=(v/w); #Frequency in the first mode of vibration(Hz)
v2=(2*v1); #Frequency in the second mode of vibration(Hz)
#Result
print "Frequency in the first mode of vibration is",v1/10**4,"*10**4 Hz"
print "Frequency in the second mode of vibration is",v2/10**3,"*10**3 Hz"
#importing modules
import math
from __future__ import division
#Variable declaration
f=0.09*10**6; #Frequency of Ultrasonic source(Hz)
t=0.55; #time(sec)
v=1800; #velocity of sound in water(m/s)
#Calculation
D=(v*t)/2; #Depth of sea(m)
W=(v/f); #Wavelength of ultrasonic pulse(m)
#Result
print "The depth of sea is",D,"m"
print "The wavelength of ultrasonic pulse is",W,"m"