Q1: In Equation No. 1, how did we get the value of 2h?Q 2: How is the equation 4 derived from the equation 1 step by step?Q3: What is the reason for the negative sign in Equation No. 2? Q4: What is the relationship between wavelength and mass?Q5:what does it mean"Where ? is the propagation acoustic wavelength which is wice the thickness of the quartz (the resonance condition verifying that the half of a wavelength is confined within the resonator)"

Sauerbrey hypothesized that for small changes in mass, the added mass could be treated in the same way as the addition of quartz. Without adding mass, the resonance frequency Dcan be willed as function of the mass m, and the thickness h as the following: =5 (1) ): sale Where A is the propagation acoustic wavelength which is twice the thickness of the quartz (the resonance condition verifying that the half of a wavelength is confined within the resonator), and v is the propagation velocity of the acoustic wave. (a) M Oscillating quartz crystal, (a) before mass addition, and (b) after mass addition Adding mass to the surface of the quartz will create an increase in thickness Ah which causes a change in resonant frequency Af.Therefore, an increase in the thickness and mass induces a decrease in frequency according to the following equation: =_E=_\"_m (2) f0 h m Note by A the area of the sensitive surface of the quartz (mnz), p the density of quartz (2.648 g/cn), v the velocity of acoustic wave (3.336x105 cm/s) and Am the additional mass deposited on the quartz (pg/ on?) Using equation (2) we can write: A_f _ Am _ 7 Am f0 _ phm _ [301/2an (3) So _ A 2f\": Elf Aep-hdm (4) The previous equation is called equation of Sauerbrey which gives the relation between the added mass and the resonance of frequency