婦 and 帚 don't sound similar in modern Mandarin due to historical phonetic changes. They were more similar
in Old Chinese. 婦*mə.bəʔ (or *tsə.-? see Min) 帚*[t.p]əʔ
Character Evolution
Oracle Bone~1250-1000 BCBronzeLate Shang~1100 BCBronzeLate Shang~1100 BCBronzeWestern Zhou1045-771 BCBronzeMid Western Zhou~900 BCBronzeEarly Spring and Autumn~700 BCBronzeLate Spring and Autumn~500 BCBronzeJin266-420 ADSealWarring States (Chu)475-221 BCSealWarring States (Chu)475-221 BCSealShuowen~100 ADClericalWestern Han202 BC-9 ADClericalWestern Han202 BC-9 ADClericalEastern Han25-220 ADClericalEastern Han25-220 ADRegularModern