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Chapter 4: 9CP (page 156)

A certain metal with atomic mass 2 脳 10-25 kg has an interatomic bond with length 2.1 脳 10-10 m and stiffness 40 N/m. What is the speed of sound in a rod made of this metal?

Short Answer

Expert verified

V=3500m/s

Step by step solution

01

Given Information

Atomic mass =2脳10-25kg

Length= 2.1脳10-10m

Stiffness=40N/m

02

Formula speed of sound in a rod

Where,

d=length

ks= stiffness

m=mass

03

calculation of speed of sound in a rod

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Most popular questions from this chapter

One mole of tungsten (6.02脳1023atoms) has a mass of 184 g, as shown in the periodic table on the inside front cover of the textbook. The density of tungsten is19.3g/cm3. What is the approximate diameter of a tungsten atom (length of a bond) in a solid block of the material? Make the simplifying assumption that the atoms are arranged in a cubic array.

In outer space, a rod is pushed to the right by a constant force F (Figure 4.54). Describe the pattern of interatomic distances along the rod. Include a specific comparison of the situation at locations A, B, and C. Explain briefly in terms of fundamental principles.

Figure 4.54

Hint: Consider the motion of an individual atom inside the rod, and various locations along the rod.

(b) After the rod in part (a) reaches a speed v, the object that had been exerting the force on the rod is removed. Describe the subsequent motion of the rod and the pattern of interatomic distances inside the rod. Include a specific comparison of the situation at locations A, B, and C. Explain briefly.

A ball whose mass is1.4kg suspended from a spring whose stiffness is 4N/m. The ball oscillates up and down with an amplitude of 14cm. (a) What is the angular frequencyrole="math" localid="1657731610160" 蝇? (b) What is the frequency? (c) What is the period? (d) Suppose this apparatus were taken to the moon, where the strength of the gravitational field is onlyrole="math" localid="1657731589019" 1/6ofthatearth . What would be the period of the Moon? (Consider carefully how the period depends on properties of the system, look at the equation.)

If in a certain material whose atoms are in a cubic array the interatomic distance is 1.7脳10-10mand the mass of one atom is 8.26脳10-26kg, what be the density of this material?

In problem P36 you can find the effective spring stiffness corresponding to the interatomic force for aluminum and lead. Let鈥檚 assume for the moment that, very roughly, other atoms have similar values,

(a) what is the (very) approximate frequency ffor the vibration of H2, a hydrogen molecule?

(b) What is the (very) approximate frequency ffor the vibration of O2, an oxygen molecule?

(c) What is the approximate vibration frequency fof the molecule D2, both of whose atoms are deuterium atoms (that is, each nucleus has one proton and one neutron)?

(d) Explain why the ratio of deuterium frequency to the hydrogen frequency is quite accurate, even though you have estimated each of these quantities very approximately, and the effective spring stiffness is normal expected to be significantly different for different atoms.

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