import math
v=5760 #velocity of propagation of ultrasonic sound wave along X-direction in m/s
t=1.0*10**-3 #thickness of a piezo-electric quartz plate in meter
lamda=2*t #wavelength in meter(since t=lamda/2 corresponding to fundamental frequency)
V=v/lamda #fundamental frequency of the crystal
print"fundamental frequency of the crystal=",V/10**6,"MHz"
import math
Y=7.9*10**10 #Young's modulus in newton/m**2
p=2650 #density for Quartz in Kg/m**3
t=0.005 #thickness of a Quartz crystal in meter
v=math.sqrt(Y/p) #velocity for longitudinal vibrations in m/sec
lamda=2*t #wavelength in meter(since t=lamda/2 corresponding to fundamental frequency)
V=v/lamda #fundamental frequency of the crystal
print"fundamental frequency of the crystal=",int(round(V/10**3)),"KHz"
import math
f=200.*10**3 #frequency of ultrasonic sound in Hz
S_a=340 #speed of sound in air in m/s
S_w=1486 #speed of sound in water in m/s
lamda_r=S_a/f#wavelength of reflected sound in metre
print"Wavelength of reflected sound=","{:.2e}".format(lamda_r),"m"
lamda_t=S_w/f#wavelength of transmitted sound in metre
print"Wavelength of transmitted sound=","{:.2e}".format(lamda_t),"m"